If you follow world cinema you should at least be aware of the Leningrad Cowboys, one of Finland's oddest but most curiously successful exports. Created for his 1989 film Leningrad Cowboys Go America by Finnish director Aki Kaurismäki, they were and still are a semi-comic rock 'n' roll band of outlandish appearance, with their dark sunglasses, unicorned quiffs and overlong winkle-pickers playing as a cartoon exaggeration of the rockabilly dress codes. Consisting of a combination of favourite Kaurismäki actors, members of the real Finnish band The Sleepy Sleepers, and former lead singer of UK punk band The Members, Nicky Tesco, they were invented for one film, but like Rob Reiner's comic rock creation Spinal Tap, they then took on a life of their own and still play concerts today, albeit with a slightly different line-up.

Artificial Eye's Leningrad Cowboys Collection is the fourth and final of their Aki Kaurismäki box sets, and one that comprehensively unites all of the director's films that feature the Cowboys, including a live concert, four music videos, and a short starring some of the main actors from both fictional features. And so, to the films themselves.

The opening scene of Leningrad Cowboys Go America is one of my favourites from all of Kaurismäki's cinema, a slow pan around a desolate tundra farmland that comes to rest on the frozen figure of one of the Cowboys, his shoes, quiffed hair and guitar all pointing skyward. In a nearby barn, the rest of the group are belting out the traditional Russian tune Oh, Field, My Field for a patiently waiting promoter, who dismisses it as having "no commercial potential," then advises them to "Go to America. They'll swallow any shit there." I've always loved that line and have had it sitting at the back of my brain for years just waiting for the right review in which to quote it. Except that it's no longer there, lost in the more accurate subtitle translations on this DVD. I miss it – "they'll put up with anything there" may be truer to the original Finnish (I'm working to confirm that), but the original translation was funnier. This is, however, the only complaint I have with what is otherwise the best-looking and sounding version yet of Kaurismäki's most internationally well known movie.

And so the Cowboys trip off to the US in search of fame and fortune, but their energetic rendition of homeland tunes fails to impress the first promoter they encounter. He nonetheless offers them a gig at his cousin's wedding in Mexico and suggests that if they want to make any headway in the music business then they need to wise up to something they have in America called rock and roll. The boys learn fast (a quick read of the right book teaches them everything they need to know) and head south with the corpse of their frozen comrade Pekka strapped to the car roof, pursued by village idiot Igor, who has been refused band entry because his balding head is unable to grow the required Cowboy quiff. The journey is funded by a series of small one-session gigs played en route, the money from which is pocketed by the Cowboy' deceitful manager Vladimir (played by Kaurismäki favourite Matti Pellonpää).

There's a case for casting Leningrad Cowboys Go America as the Finnish The Blues Brothers. Both employ a thread-thin storyline to transport their respective oddball musicians across America with pauses for musical numbers and inspired silliness, and both are hugely enjoyable and sometimes very funny films. But there the similarities end. Where Landis revels in the comedy of excess, Kaurismäki employs a resolutely minimalist approach, and does so to typically delicious effect.

The one joke that doesn't click here is the suggestion that the Leningrad Cowboys are the world's worst rock 'n' roll band, and that's only because they're actually rather good, certainly decent enough for us to believe in the positive audience reaction they intermittently provoke. Their ludicrous appearance is good for about two gags by itself, but Kaurismäki extends the mileage through their sometimes hilarious arrangement in frame, lined up like peculiar sculptures against classic American buildings and landscapes, compositions that occasionally resemble a playful surrealist reworking of Edward Hopper paintings.

Cultural elements are inevitably brought into play, with the Finnish fondness for heroic alcohol consumption giving rise to a laugh-out-loud visual gag involving empty beer cans, and you can have fun reading a political element into Vladimir's exploitation of his workers and the uprising it eventually provokes. Intermittently, the film captures the sense of strangers in a strange land with surprising poignancy, but Kaurismäki avoids the temptation to send up the locals, a reflection of his own fascination with particular aspects of American culture. The through-the-car-window drifts past industrial and residential locations have flavour of Jim Jarmush about them, a debt Kaurismäki acknowledges by casting Jarmush himself (who borrowed actors from Kaurismäki for the Helsinki sequence of Night on Earth) as the first of a pair of car salesmen the group are fleeced by en route.

Possibly the most good-natured film in Kaurismäki's enviable oeuvre, Leningrad Cowboys Go America is a surreal, imaginative and frequently funny tale of culture collision, one that avoids condescension and stereotyping and whose oddball central characters remain unwaveringly likeable throughout. And with much of the dialogue delivered in English, the way is open for even the culturally unadventurous to appreciate this one.

It had to happen, I guess. We're four film collections in and I had still yet to see a Kaurismäki film I didn't like and admire immensely, then along comes Leningrad Cowboys Meet Moses. Of course, there's the argument, perfectly valid, that that Leningrad Cowboys Go America didn't need a sequel. One thing's for sure, it didn't need this sequel.

It's five years on from the first film and the Leningrad Cowboys, who were on the brink of success in Mexico, have fallen victim to the destructive effects of Tequila. Several deaths later, the survivors have fled into the wilderness and gone native, growing large moustaches to match their still outlandish hair. Then one day their former manager Vladimir returns. Heavily bearded and proclaiming himself as Moses, he assures the others that if they obey and follow him, he will lead them back home. Before departing, he climbs the statue of Liberty and steals its nose, news of which attracts the attention of the scheming Johnson (André Wilms), who is soon on their tail. Aided by brothers from the homeland, the Cowboys make their way across Europe, playing gigs at sometimes unlikely venues as they travel.

The plot is as thin as that for Go America and involves a similar cross-continent journey, but here the Cowboys get to stop off at a number of European locations, including France, Germany, Czechoslovakia and Poland. Politics and religion and the uneasy relationship between the two are rather crudely lampooned (although I did rather like Vladimir's version of the miracle of the burning bush), and there's plenty of the Cowboys' trademark absurdity on the way. But by broadening this to include Airplane-style daftness (Vladimir flies to Europe on the wing of the plane in which Johnson is travelling), it somehow loses its charm and illustrates too clearly that absurd is not amusing by default.

It's a fine line that separates a groan from a guffaw, and my problem with the film is that I just don't find it funny, and with little in the way of plot to fall back on it really needs to be. I'm personalising that comment because what amuses one person will inevitable annoy another, and while no-one seems prepared to claim that Meets Moses is equal to the original, a few have admitted to enjoying it nonetheless. Evidence for the prosecution, however, is provided by a direct comparison to Go America, whose warmth, inventiveness and humour this sequel certainly tries to recapture, but in a manner that feels uncomfortably like a once-funny comic dying on stage with material he would previously have rejected.

Total Balalaika Show is a record of an open-air concert performed on 12th June 1993 in Helsinki by the Leningrad Cowboys and the Alexandrov Red Army Chorus and Dance Ensemble. And don't let Kaurismäki's director credit fool you, this is a straight up concert film in the classic style. And it's an absolute blast.

Dumping the off-tune vocals of Leningrad Cowboys Meet Moses, the group here establish their rock 'n' roll credentials with a string of energetically delivered cover versions of songs by artists from Tom Jones to Bob Dylan to ZZ Top. This in itself would be engaging enough, but they're not alone on stage, not by a long shot, and this really does change everything.

It's hard to imagine a more unlikely pairing of talents than the shade-wearing, spiky quiffed and pointy shoed Leningrad Cowboys and the uniformed Red Army singers and musicians, who holler out the choruses of Delilah and Gimme All You Lovin' as if performing songs from the homeland to stir the emotions of comrades on the eve of battle. The rock numbers alternate with traditional Russian folk anthems such as Kalinka and Oh Field, My Field, where the Red Army Choir and their full voiced soloist are given the stage, while the Cowboys either stand by respectfully or lie down flat and tap their overlong shoes. Several numbers are enlivened further by a bevy of Russian dancers – with Jewellery Box it's they who are the stars – while the boisterous Kalinka gives the Cowboys the chance to try their hand at Cossack dancing, their efforts momentarily prompting the Russian soloist to stumble in his singing and laugh.

The concert is at its most joyously surreal when the soloist and the Cowboys share a song – you haven't lived until you've watched a middle-aged Red Army officer operatically belting out the lyrics to Happy Together alongside his unicorn-haired Finnish companions. It's funny and entertaining and actually rather inspiring, as nowhere will you find a more exuberant celebration of that special relationship that has existed for so long between the two nations. This is reflected in the reaction of the audience to both parties – they may have come to see the Cowboys, but they still shout for the Red Army Choir and Dancers. The inevitable "wish I was there" nag that dogs all such films worth their salt aside, Total Balalaika Show is a wonderful record of a glorious event, and genuinely more fun than any other concert movie I can readily recall.

The high standard set by Artificial Eye's previous three Kaurismäki box sets is maintained by the close to faultless anamorphic transfers here, with contrast, sharpness and colour all excellent and hardly a dust spot in sight. Even the short films look terrific, with only the 4:3 L.A. Woman having a hint of softness.

Both Go America and Meet Moses have sparkling Dolby 2.0 surround tracks that shine in their clarity and clean separation, and make subtle but very effective use of the surrounds. Surprisingly, Total Balalaika Show has only a Dolby 2.0 stereo track – it's a good one, but a 5.1 mix here would have more clearly informed the neighbours how much I was enjoying the show.

A lovely bonus with this set is the inclusion of five of Kaurismäki's short films, four of them music videos for the Leningrad Cowboys, the other made shortly before Go America and featuring many of the actors who appear in that film.

Rocky VI (8:17) (1986) is set to music but is effectively an extended gag on the Finnish fondness for food and alcohol consumption, and those Rocky movies in which the Italian Stallion takes on (and defeats) nasty foreign boxers. Here Rocky (actually spelt Rock'y) is a hard-training but hopelessly weedy American fighter, while his Finnish opponent is an oversized drinking and eating machine who punches seven bells of crap out of the American the moment they enter the ring. Kaurismäki regulars Matti Pellonpää and Mato Valtonen play the trainers.

Filmed in black and white, Thru the Wire (5:32) (1987) is a poignantly handled story of a man on the run (Nicky Tesco), who dreams of being reunited with his girl and gets to take the stage with a small group of Leningrad Cowboys to express his feelings and experiences in song.

Also in monochrome and gorgeously shot, Those Were the Days (4:27) (1991) is built around a performance by the group in a Parisian café, in which a super-quiffed Elvis is tending bar and the owner is the female Cowboy (played by Kirsi Tykkyläinen) from Total Balalaika Show.

These Boots (4:35) (1992) claims to be a history of Finland from 1952-1969 and is a briskly staged story of one man's life. He's played by Mato Valtonen at all ages, including as a baby, as strangely surreal an image as you'll find anywhere on this collection.

Finally we have L.A. Woman (5:01) (1987), the most straightforwardly staged and shot of the bunch. Effectively it's just the group, fronted by Nicky Tesco, performing the song on stage, but is also a rare demonstration of how good the Cowboys could be when they played it straight. It's a belting version of the song, the on-stage imagery briefly interrupted for a touch of political commentary when images of war victims are juxtaposed with the smiling face of Ronald Reagan.

The Leningrad Cowboys Collection is currently being suggested as the fun alternative to Christmas pantomime and I have no problem with that. Sure, Meets Moses doesn't work for me at all, but I'd be recommending this set on the basis of Total Balalaika Show alone, and you've never seen Go America look and sound as good as it does here, AND there are five shorts included. How could you not want this? Highly recommended.