Strove (diemachonto). Imperfect middle of diamachomai, old Attic verb, to fight it out (between, back and forth, fiercely). Here only in the N.T. It was a lively scrap and Luke pictures it as going on. The Pharisees definitely take Paul’s side.
And what if a spirit hath spoken to him or an angel? (ei de pneuma elalēsen autōi ē aggeloṡ). This is aposiopesis, not uncommon in the N.T., as in Luk 13:9; Joh 6:62 (Robertson, Grammar, p. 1203). See one also in Exo 32:32.