I don't want to overwhelm you with work.
He did not want to overwhelm the students with homework during homecoming.

The rising tide threatened to overwhelm the flood defences.

To overwhelm means to cause someone to be overcome with emotion, so that they cannot control themselves. To overwhelm with humor would be to us humor in order to cause someone to laugh uncontrollably. The implication here is that the other person is hostile, and you overwhelm them with your sense of humor.

Some synonyms for "engulf" are:

Steep, overwhelm, engross, immerse, absorb, plunge

underwhelm