Are two dollar bills from the 1940s and 1950s worth anything beyond face value?

no

MoreActually, YES, but not a huge amount. It depends on the bills' conditions and series dates. You can find some representative values at the Related Question.

And FWIW, there aren't any US bills with series dates in the 1940s. Back then the practice was to run a "series" until there was a major design change, and because bills weren't redesigned very often in the mid-20th century, a single series could run for as much as 30 years without a date change.