Question is what setting you are using - Pathfinder's default Golarion, homebrew setting or something else?
Unless this is homebrew any such hybrid would be unnatural - probably a result of magical or alchemical experiment. If you GM homebrew setting you might add a note that strix are capable of corssbreeding with elves, humans or half-elves. Or resort to magical experiment if you don't want such hybrids occurring naturally.
If you are GMing Forgotten Realms you could try to convince her to play Avariel (Winged Elf) instead.
Either way you can use the rules available in Advanced Race Guide race builder to create a strix/(half)elf hybrid (or winged elf in case of FR).
A Wizard Did It.
Well uh...justifying it for mechanics/stat reasons, justifying it for flavor/rp reasons, or both?
Get a tape recorder, get the player to explain the birds and the bees between an elf and a race of xenophobic flying people, and then play it back to them three days later? I find that the embarrassment of actually hearing your silly ideas tends to discourage this kind of thing.
Seriously, how does this play out? Normally, a strix would fly away from the Enemy Mine situation which would lead to this. When you say wingless, does this mean a subspecies of Strix born without wings, or just the half strix lacks wings? If it is the former....what is left when you remove wings and xenophobia from a strix?
The easiest solution I can come up with RP wise to explain this mess is a preexisting married elf couple and a reincarnate spell. Even with elves, most do not get up to a high enough level to get the wish to fix that little problem.