I need to know if this version of the name Elise is too strange.

Here's the reasoning: Our son was named after my husband's great-grandfather, but we want to name the next one (due in November) after my side.

My grandmother is 100% Finnish and her name is Aili. I don't really like it for a first name, but I like it for a middle name

SO, if it's a girl, it will be Eliisa Aili. I guess it's a really popular name in Finland right now, and I love Elise.

Will I be branding her with a really strange name? Or just ... unique? 

I don't think it's strange at all.  I am the queen of "normal" names.  So if I'm not alarmed, you're fine! 

I think it's great, totally not strange, just normal enough to be unique.

Not strange at all.  It's unique but not off the wall crazy.  I like that the middle name is after your grandmother too.  : )