Reagrding the gift thing.
I did the same. Took up quite a fair bit of my luggage with gifts actually. And never ever met my neighbours, or anyone likely to get those gifts. I ended up using some myself and taking some back home after two years.
Its not that I didn't want to meet my neighbours. Its that they never did anything to meet me or interact with me etc. I actually found this to be quite common with foreigners I spoke with. Most had never ever met their neighbours, nor had the
gift giving gone on, and it wasn't for lack of trying by the foreigner. But then I'd read that the custom as a whole was dying in Japan.
I dunno, just dont get too carried away or you might be using a lot of luggage space for things you could use.
Reagrding giving gifts to students. Don't. Nova will get very suspicious about and its against the rules anyway. Maybe a few gifts for the branches Japanese staff. Maybe. But even then...
As for things from home. Toothpaste and if you use them, good quality toothbrushes (if you're fine with cheap and nasty stock standards don't worry). Deoderant. Condoms. Decent Aftershave. If you're into it and have the cash to afford it (maybe at duty free) mens cologne's like CK or Ralph Lauren stuff as its rather hard to come by in Japan. Smelling good and looking nicely groomed will instantly elevate you amongst a bit higher than pretyy much every salaryman and most foreigners you'll meet. Haha.
English language software if you intend on using a PC.
Oh yes. If you have shaved or cropped or buzz cut hair, try and pick up a pair of ahir clippers
That have international voltage conversion built in. They aren't common in Japan, hair dressers barely use them and you'll save a bundle of money in the long run.