Are you looking for something like this?
select *
from MY_TABLE
where (id, name) in ((1,'new'), (2, 'old')) and
date between effectiveDate and termDate
This looks for the pairs in a list and then checks for the dates between a range of dates.
EDIT:
I think you want to break this into multiple clauses, one for each set of values:
where (id = 1 and name = 'new' and date between eff1 and term1) or
(id = 2 and name = 'old' and date between eff2 and term2) or
. . .