IIRC 0 ohm resistors or "links" are used as short circuit jumpers of a sort. Sometimes it is easier to install them than very short pieces of wire, especially in SMD applications.
All they have to do is handle the current in the design application. Current and voltage will determine the power rating (P=I^2R).
I do find it funny that they have a power rating. I suppose that's more about the size they are than anything else.
The teflon coated wire we provide is super nice, but it's also hard to strip the ends of a really short piece, so a 0 ohm resistor makes things much easier.
I deal with that by stripping the entire length of wire that I need, cut the removed teflon jacket to desired length, and slide back on. Being teflon, it slides on easily.