Looking for Woody Allen movie old school music


Apologies if this sounds moronic. I am trying to find the singers and songs from Woody Allen movies such as Anything Else, Magic and the Moonlight, whatever. The ones that don't have published soundtracks. W loves it. Please help me out
shugho
Casey, thanks! This is part of an effort to make some recent purchases more appealing :)

Thanks Jazzcourier, for the detailed explanation. I am aware of some of the artists he uses (Cole Porter, Billie Holiday) but some of the songs/artists I heard recently were unfamiliar to me. I will look up the artists you suggested. Do agree that his music plays a big part in the appeal to especially his recent works, which seem to be targeted more for the mainstream. Wonder if he grew up listening to them.

Dweller, duh! This is why I rely on opinions as I am slow.

Alexatpos, another artist I have not explored, in spite of my varied explorations. Looking forward to it.

Thanks all!
Yes, Bix Biederbecke is definitely one of the ones I was looking for, along with some old school vocals, which I should be able to find from the credits!
Goodness, it is hard to find the original albums. Some are 78s and I only have a vinyl player that will play 33.5 and 45. I am enjoying trying to find them though.
Found the following artists

Ruth Etting - The female vocalist I was looking for :)
Smith Ballew
Ray Noble and Al Bowlly
Nat Shilkret and Victor Orchestra
DeParis brothers

Next challenge is trying to find the albums - Amazon is not working well for this type of music :) Need an Amazon vintage!