I've little to no experience of church sound reinforcement specifically, but as with all things to do with sound reinforcement the answer will depend on your budget and what the venue/audience can get their heads around and will tolerate. It satrikes me that you're about at the point where sensitive sound reinforcement starts to become necessary.
Keyboards that put out huge volume differences between settings or single notes/chords are far from uncommon and unfortunately many keyboard players (like guitarists with big volume jumps when they step on some pedals) don't necessarily see why they should pay attention to that problem and take steps to deal with it themselves. The ideal solution is to re-train the musician, not just about volume but about leaving musical space for others, sadly that's often also the hardest solution to achieve.
If the organ isn't entirely acoustic (e.g. a pipe organ of the kind that turns up in British churches) and happens to go through seperate amplification (that's not built into it) one easy solution might be to strap a limiter/compressor between organ and amplifier. Wouldn't need to be expensive, any half decent rack compressor set with a high enough threshold top just catch the too loud bits should work. Just watch out for the increase in RMS volume if the organist keeps pushing out the volume. Failing that plug the organ into a mixer and ride the channel volume as required.
Failing getting the organ volume down, the choir has to get louder.
There are quite a few low profile dynamic mics (small capsules on thin, dark coloured stands) on the market that might do the trick for the choir. Maybe one each, or maybe just a couple or three at a distance might do the trick. Much will depend on training the choir into using microphones of course - particularly that they can't wander around in front of them or turn away from them and expect things to "just work" somehow. Another option is to hang overheads over the choir which might be better if the singers are inclined to be a bit mobile. Watch out for hand clapping though - it can cut through anything and is surprisingly loud compared to singing. Again, simple compression might be useful. Even one of the mixers that has "one knob" compression on the mic channels.
People passing a mic around is always a problem, there are people who no matter how often you explain it to them will simply never get the hang of any microphone technique. I've done conferences where speakers were all told when given the mic "hold it pointing at your mouth at a distance of three or four inches and speak normally like you would to someone standing next to you". So one speaker will hold the mic next to their lips and shout at it then the next speaker holds it at around waist height facing the audience and almost whispers.
Ideally I guess you do what most places dealing with several speakers do and put the mic on a stand (maybe hidden into a lectern or something) and the speaker goes to the mic to speak. The lectern then gives them somewhere to put notes down and keeps them at a sensible distance from the mic. . An omni-pattern mic on a stand can be useful if the speakers form a crescent round it, but not if you don't want any bleed-through from people near the mic.
Then there are the ones who tap the microphone pop shield asking "is it on" despite just seeing five people use it....
Really the best answer is to have someone with fast reflexes sitting at the mixer and actively riding the channel fader(s) and mute(s) all the time.