Janice and I come from years of playing 3-6 chord bluegrass, blues and classic country -- a lot of what is now known as Americana. Beyond that we get a bit lost with neither of us knowing any theory. We are working on a PD song published in 1914 called Ballin' The Jack. It introduced a new dance and has been done by everybody from Judy Garland to Dean Martin to Pearl Bailey to Fats Domino to show tune formats. We tried some of the very simple progressions but tend to like the more early jazz versions. Below is a 16 bar verse we found presented as being in G. The chords seemed odd but sound pretty good so I looked at more versions and many of them although in other keys were relatively the same as this.
So I'll show my ignorance (ample precedent) --- aren't the E, Eb and F# chords odd for the key? Thanks for any help and perhaps my ignorance has given you a good laugh!
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I had thought it was the wrong key until I found it again with a stated key of G. At which point I assumed I must be missing something But yeah the progression works.
Bud
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Can you save us some time and post a BIAB song with this progression?
I don’t want to take up your time. Thought it would be a quick question. Sorry.
Janice
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Thank you Matt! We appreciate it. I dropped it into BiaB along with the chorus.
Here it is with the verse and the chorus. The chorus does resolve to a G FWIW.
J&B
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One of the basic theoretical shortcuts for helping to analyse music is that when looking for modulations, isolate the 7th chords. If these chords form a V7 to I (e.g. G7 to C) or V7 to VI (e.g. G7 to Am), then the music has been temporarily modulated.
Often such temporary modulations occur so quickly that there is no accompanying (pun not intended but I like it) feeling that a modulation has occurred.
So with the above couple of thoughts in mind, my take on this is...
At the end of this progression we see "D7", if the next chord is "G" then a V7-I progression has occurred and the music in the subsequent section that's not provided is indeed in the key of G major (or G minor if the chord following D7 is Gm -- this is still a I-V progression in a minor key).
Now for the chord progression...
For ease of reference, I'll ignore the 7s and just look at the major/minor chords.
If I consider E as a tonic (i.e. E = chord I), Then the first four chords E-F#-B-C is a I-II-V-bVI progression.
Now if the C chord is a pivot chord and it becomes chord IV in the key of G (i.e C changes from bVI in the key of E to IV in the key of G) , we have the progression C-A-D-Eb expressed as IV-II-V-bVI. A pattern of II-V-bVI now seems to be emerging... let's continue and see what happens
If the C (second line of chords, chord #3) now starts out as IV in the key of G major and changes into into bVI in the key of E major (i.e. it's another pivot chord), we have the chord progession C-B-E-F#-B-C (in the key of E major) as bVI-V-I-II-V-bVI.
So it looks like the above progression revolves around a II-V-bVI progression in the keys of E and G major with chord II being the major chord rather than the usual minor chord that's found on the second degree of the major scale. The C chord seems to be the pivot chord that allows transition between keys.
So below is a picture that I hope summarises my interpretation (the chords with asterisks seem to be pivot chords -- that is they straddle two keys and allow for a change from one key to another)...
Just my thoughts.... I could be totally wrong! Noel
P.S. Here's a pretty good article on using bVI chords in music.
I started down the analytical route Noel took, but decided the composer is being too cute. That's why I keyed the changes into BIAB and lived with it a few minutes. This convinced me it's in E.
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Maybe this is a simpleton approach but looking through the chord progression and not seeing a single instance of a G chord, my brain has a hard time believing it’s in G.
The more I think about this, this more I'm of the opinion that this verse sets out not to have an easily identifiable tonal centre so that when the song arrives at the chorus, the sense of 'home base' is amplified and felt strongly.
I found the image below of a version that's written in the key of G major. The chords you give are a minor third lower than the chords on this music. This suggests that your chords are in the 'overall' key of E major.
Notice how the at the bottom right of the below image, there are two flats in the upcoming key signature (this suggests Bb major) and the last chord is F7 (which leads to Bb major as a V-1 progression).
Interestingly if I go down a minor third from F7, I get D7 (the last chord in your above post). Also a minor 3rd down from Bb is G -- also in keeping with your post.
So... using the image below, your chords would seem to be in E major but drifting every now into a slightly hinted key of G.
You might find that you get better results from BIAB if you set the key for the verse to E and the key to the chorus to G. My experience is that such settings help BIAB isolate which chords will work best.
I suspect (maybe wrongly) that the suggestion it is in the key of G is incorrect.
In the diatonic scale, the intervals for an E major chord would land on a G# as the first triad. I like to think that discordance is allowed, but to me this is a little too challenging.
The only chord that comes close to suggest G Major, is the Eb which would have G natural as the first triad and include a D natural as the 7th.
Even the C7 would introduce a Bb, which would lead more to a G minor key.
Regardless, Bud, there are no stupid questions (well not on this forum anyway). Moreover, I think you've already identified that this progression is peculiar for a tune supposed to be in the the of G Major and suspect that it is incorrect.
My definite guess is E Major.
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I very rarely use styles. Having worked with RTs and RDs for years I like to make up a band per each production.
This song will have a rockabilly bass, Nashville Drums, a jazz rhythm guitar, a 40's boogie piano (Midi Super Track ultimately), a fiddle chop rhythm and either a gypsy jazz or a western swing fiddle for the solo. As always Janice will do the vocals.
Here is a very ROUGH representation of how the chords sound with what will become the band. Please note the word "rough" as I have done NO track comping which I nearly always do to remove funky notes, improve segues, enhance fills, etc., and make the tracks more compatible with the vocal.
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The thing I have learned about music in all the years I have studied theory, (several years of study on theory) and played my instruments both with and without lessons. My piano teacher was big on explaining the theory behind the music to make it understandable, and I was in a music theory class and that's all we studied, and worked things out with a piano..... It breaks down as follows.
There are essentially TWO rules in music.
1. There are rules in music that must be followed. 2. There are no rules in music and thou canst doth whatever thou wish.
So, no matter what the key and what you expect to hear or to have happen next, it doesn't matter as long as, in the context of how it is used, it sounds good. No chord or progression is off limits if you can make it work.
You can find my music at: www.herbhartley.com Add nothing that adds nothing to the music. You can make excuses or you can make progress but not both.
The magic you are looking for is in the work you are avoiding.
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But yeah the progression works. 
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