What key is exit music for a film?

Firstly, remember that music theory is only (or predominantly) about describing what goes in music. That's ALL music, assuming it sounds OK, and (I guess) assuming it's within western musical culture. (The body of knowledge we call "music theory" can often address music of other cultures, but that's not really what it's designed for. Those cultures have their own theories...)

Secondly, whenever you think something "shouldn't work", that's because (a) you've read too much music theory and (b) you haven't read enough music theory. ;-) I.e., you think that what you've read (which roughly equates to diatonic harmony) is all there is to say.

Thirdly, what "sounds good" is stuff you've heard before. Obviously there are some things you've heard often, and other things you've heard less often. It's the latter things that make music interesting - the less trodden paths, if you like. (I.e., they've still been trodden, just less often.) Music theory will have ways of addressing those, you just haven't yet encountered the relevant concepts. Except now, in this thread, you have... ;-))

If you ever heard anything in music you'd never heard before, you'd probably think it just sounded wrong: it would be baffling, and might not sound like music at all - it certainly wouldn't "belong" aurally, not just theoretically.

So - there are plenty of terms to describe what Radiohead are doing. The issue is that none of those explain why they sound good. They're just labels. (You can't explain why food tastes good by listing the ingredients - because you then have to explain why those ingredients taste good...)

It might help more to look at what's familiar (common) about how they put chords together, not what is unfamiliar. To take Exit Music For a Film - here are the chords in order:

Bm-F#-D-E-Bm-F#... = all key of B minor so far. F# is the harmonic minor V chord, and E could be a B dorian IV chord - extremely common "borrowed chord".

B-Bsus4-B = resolution to a major tonic instead of minor. Sometimes known as a "Picardy 3rd", although that normally only happens right at the very end of a piece. Notice how this "brightening" of the mood coincides with the lyric "we escape". I.e., things are looking up; the major chord expresses that.

The second section starts on Am, which is (admittedly) a surprising lurch from B major. And yet, we hear those two chords often in the key of E minor (Am=iv, B=V), so they're not total strangers to each other. But also, that lurch to Am - creating a tension - expresses the sentiment in this section "breathe, keep breathing, don't lose your nerve... I can't do this alone".

The Am moves to E, echoing the opening Bm-F# change (minor key i-V) - but then goes back to Bm and F#. But again that works quite smoothly because in the first section the E major was also followed by Bm and F#.

On the repeat of this section, the opening Am sounds even stranger because now it's following F#7. There are few scenarios where we'd normally hear Am and F#7 together. But at least Am and Bm share the G major scale. And we can call Am a "borrowing from B phrygian", phrygian being a suitably darker mode (to suit the lyric at that point).

But there is voice-leading between F#7 and Am too. Voice-leading is what you might call the "secret mechanism" behind how all chord changes work, the normal ones as well as the abnormal ones. In this case, both chords contain E (shared tone); A# moves down to A, and C# moves down to C. That only leaves the F#, with a weak-ish move down to E. Voice-leading over-rides all issues of key: we perceive shared tones in particular, but we also perceive (and like) semitone shifts, especially downward. Voice-leading is a kind of pied piper, leading us seductively out of the "town" of diatonic key...

In the third section ("you can laugh"), we have another interesting mix of chords: Bm-C#7-F#-G. New entry C#7 is V of F# which - assuming Bm is still the key - is a "secondary dominant". Again, that's only a label - which recognises that this is a common practice, without actually explaining how it works. How it works, of course, is voice-leading. ;-) This time vocal follows the chromatic descent from F# on the Bm to E# on the C#. In the fact the vocal ties these four chords together very neatly. On Bm-C#7, it runs D-F#-E#. On F#-G it's a scale degree lower: C#-E-D.

G is the natural VI chord in B minor; but it continues to the next line and leads to C (the word "rules"). We could say C is "borrowed from B phrygian" (like the earlier Am), which is again just a label recognising the fact that this is a "common practice". But IMO in this case we just accept the G-C change as one we hear very often outside of this key.

IOW, one very simple way of looking at these changes is that every pair of neighbouring chords in this song belongs together - they occur commonly in the same key. That (along with voice-leading) is why we're persuaded they all "work", because each step through the progression sounds logical and familiar in itself. Just to take this section:
Bm-C#7 = key of F# minor
C#7-F# = key of F# major
F#-G = key of B minor
G-C = key of G or C major
... then, however we get the C-F#7 change, which puts us back in the B minor ballpark, exposing the C as more strange than the simple pairing with the G led us to believe. Still, the voice-leading explains it: the melody falls a semitone from G ("and") to F# ("wis-"), while the C rises to C#.

And from there, we're back with the sequence of the first section, while Thom Yorke is an octave higher ("now, we are one..."). Now we get the final "bright" picardy 3rd resolution to B major as he "hope[s] that you choke". You might think that such a sentiment requires something angry and dissonant, but of course this is a positive thing for the protagonist. "We are one, in everlasting peace", so the rest of you can go to hell! :-)

TL;DR: chords connect via voice-leading. Diatonic key relationships matter less, if at all.

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