The HC page has some great descriptions.
Flanger vs Chorus - I tend to use Flanger as an "effect" due to it's unique sound, and sparingly. (the "whoosh" as described in HC is very unique)
Chorus produces a similar but more "chimey" sound. I use a Line 6 Spider amp and on the "clean" amp modeler add a little in, almost always have a little on, when playing full rhythm chords, as it thickens the sound. More can be very distinctive, kind of organ-like.
If you're playing with a second guitar, especially if it's an acoustic guitar, the chorus will help distinguish the electric. If there's a piano playing too an electric needs to avoid cluttering up the overall sound with more of "the same thing", and you can actually play less straight on rhythm and do more single strums or other parts to fill out the arrangement. If you're the only guitar, the chorus makes the chord stuff nice and full.
Reverb - actually contributes to your "placement" in the sound image. It's the sound of your guitar bouncing off the walls and ceiling and "reverberating" back at you. Amps often have a Reverb unit so you can shape your sound.
If you're in a large room, or church, be careful how much you add in, as there's normally a lot of room reverb already. In a room where there's not a lot of obvious reverb, it will help to distinguish your guitar sound. It's a really useful effect.
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Overdrive" (if you've got an OD or Gain knob it's probably driving the preamp) is a form of distortion. Distortion occurs when some stage of your sound is over taxed and pushed beyond it's normal range. Like - if you have 5 watt amp and turn it all the way up and turn your guitar all the way up, there will probably be some distortion of the sound, either preamp, amp or from the speaker. Not necessarily though - and if you have a 1,000 watt amp, it's going to be difficult to get that puppy to distort, unless you're outside or in a reallllly big room.
A lot of amps have a gain knob, where you can turn up the preamp stage and run it hot, while adjusting the overall volume out from the amp separately. There's different ways to achieve that and I'm not an expert in any, but it's something to play with and see if and when it works for your song material.
I'm not a believer in forcing "distortion" into every song - it really depends on the tune. If it's a standard hymn and I'm trying to find a good sound, I probably won't go for the distortion. Other stuff, yeah. People's ears are pretty used to hearing that sound today in pop/rock/etc.