How to respond to wedding gifts from extended family?

While my father is Japanese I've always been much more connected with my mother's culture so situations like this leave me unsure on how to respond.

I left Japan at 18 to go study overseas and am coming back now in my late 20s. I recently got married and my father siblings who told their kids and now gifts are coming in left and right and while I appreciate it, I feel kind unsure about how to respond, we didn't have a ceremony over here and we were not planning on having any sort of celebration in Japan either. When I asked my dad about it, he said "not to worry about it".

If they were just small gifts I imagine a thank you call would suffice but I fear most of them won't be, I know I received a rather pricy kitchen robot (~¥300 00)

Any insight on how to deal with this would be helpful!