What is the difference between the vowels in "sole" and "solo"?

In some dialects of American English, if there's an /l/ at the end of a syllable after particular vowels, the /l/ turns into /əl/. This means that pairs of words like bowled and bold will get pronounced differently. Listening to a few pronunciations on the internet, this doesn't generally seem to happen in British English (there are also lots of Americans who don't do this).

This generally happens for the vowels found in the words soul, fool, file, foul, feel, fail, foil, and sometimes pal.

In solo, the /oʊ/ and the /l/ are in different syllables, so the /oʊ/ is pronounced normally. In soul, the /l/ ends the syllable, and can turn into /əl/. So what you're hearing is essentially the triphthong /oʊə/ before the /l/.