How is the AND/OR operator represented as in Regular Expressions?

Not an expert in regex, but you can do ^((part1|part2)|(part1, part2))$. In words: "part 1 or part2 or both"

'^(part1|part2|part1,part2)$'

does it work?

Does this work without alternation?

^((part)1(, \22)?)?(part2)?$

or why not this?

^((part)1(, (\22))?)?(\4)?$

The first works for all conditions the second for all but part2(using GNU sed 4.1.5)

I'm going to assume you want to build a the regex dynamically to contain other words than part1 and part2, and that you want order not to matter. If so you can use something like this:

((^|, )(part1|part2|part3))+$

Positive matches:

part1
part2, part1
part1, part2, part3

Negative matches:

part1,           //with and without trailing spaces.
part3, part2, 
otherpart1