Along with the strong form as transcribed in post #2 above, it is very often pronounced in its weak form, with a schwa: /ʃəl/.
I think this schwa pronunciation is very rare in American English. When AmE speakers use "shall," we tend to do so deliberately, and the deliberateness manifests itself in somewhat emphatic, un-schwa-like pronunciation.
I have wondered if BrE speakers tend to use the schwa pronunciation when using "shall" as a run-of-the-mill future auxiliary. Would anyone care to answer that, even if only speculatively? I'm not looking for statistics.
My "theory" is that one of the reasons almost no AmE speakers use "shall" as a run-of-the-mill future auxiliary is that we do not naturally use it in a casual, de-emphasized manner. We pronounce in"shall" a stilted way, so it seems stilted to most of us.
For most AmE speakers, saying something like "I shall be home shortly" carries a level of formality analogous to going to the beach in a tuxedo.