Well, it is a Hebrew name - why shouldn't it sound Jewish?
Theodora is much more likely to be used by Christians than Jews (though a Jewish atheist friend of mine famously married a woman named
Christine!) so maybe consider it as a mn, unless you've got that sorted out for family reasons or something.
OTOH, I like both
Ilan and
Ilana, and
Ilana goes very well with
Theodora, I think.