Simple answer: Yes.
They cannot be elected twice to the same parish (ward 1 and ward 2), but there is no restriction - and in rural areas quite common for people to be elected to two parish councils - it can help with work between the two parishes for events and fundraising.
There are 4 qualifications to be elected: Live, Work, Land, Distance, mean that you can live in 1 parish, work in another, own land in a third and live within 3 miles of the 4th parish. (as long as you have done each thing for at least the last 12 months).
I have stood in elections for 2 different parishes, both were on the Distance rule (I was 1 month short of being able to use the work rule). I live 200yds from the other parish boundary.