Yes, we give housewarming gifts. These days, unless the couple really don't have anything, it's likely to be a bottle of wine or some flowers for the 'lady of the house'.
Marauder times ... Not so much the wine (unless it's a housewarming party) but maybe a revolting ornament, or a coffee table book (that's a stylish looking book that looks good but no-one ever reallly reads)
When we moved house when I was seven, we got about five different potted plants from our new neighbours, so yeah we give them.
I can imagine wizards giving housewarming gifts. I think because there's so few of them, another moving into the area would be quite a novelty. I can see them giving things like household potions and other more magical type of things. I don't think it's too much of a Muggle thing; it's a nice thing to do and gets you off on a good start with the new neighbours. I think it's something that wizards might do without realising Muggles do it as well.