Can "intrude" be used transitively?
Solution 1:
"Intrude" is an intransitive verb so needs the preposition following. I've never seen "intrude" used with any preposition other than "on" but that is a stylistic matter, I think.
"Invade" is transitive and should not take the preposition.
Solution 2:
There may be instances where transitive use is possible, but normally a preposition is obligatory after intrude.