When I take pictures in church for events.
-No flash is best - IMO, need a prime lens, my Canon 50mm f1.4 does decent, if you don't have one try and borrow/rent. Or a fixed 2.8 wide zoom.
-I agree on test shots for lighting/conditions/composition. IF not days before than still before the start of the event. Yes, it's hectic but that's part of being a photographer.
-I've had success with setting shutter speed at 1/30 sec- that freezes people motion enough in a church setting, hand held with IS on, ISO 800. Again, test shot to confirm your exposure, shooting in RAW you can PP if slightly underexposed. My T1i looks grainy at ISO 1600, so I try and stay lower than that.
-Get in 1st/2nd pew, if you have one a monopod is sweet to steady your shot, especially if you take combination of stills and video. Nobody likes looking at shaky video.
For ref, here is a picture taken during xmas service last year
50mm f 1.4 lens, shutter priority @ 1/60 sec, ISO800, my T1i camera selected f2.2 for this shot