In my experience, "superset" is almost never used, though I have come across it before (usually not in a formal context, though). Instead of saying "A is a superset of B", it's customary to just say, "B is a subset of A".
I've never heard "supersequence".
I suspect that, in both cases, it's because it's not particularly meaningful to talk about all the supersets or supersequences of a set or sequence. On the other hand, we commonly (though not necessarily) say "x<y" or "x>y", rather than "x<y" or "y<x" (i.e. we use both "less than" and "greater than", not just "less than"), because it is meaningful to talk about all the numbers greater than y.