If I'm playing a caster, after I get my core items, I'll be on perma Blue.

I mostly fix myself on elixirs on TT, not so as much on SR.

And it depends on what I'm playing, lets say green elixir is a must on tryn or similar chars.

Blue is hilarious on LeBlanc during the midgame, and necessary during endgame so you can spam your e and r to control enemy movement.

When playing Galio, I'll grab one or two Blues for the laning phase, and one or two Reds for team fights.

If I had enough gold to spare, sometimes both.

Other characters I have different times/uses for them, but I buy them too.

Yes. There is absolutely no reason not to be, especially if you need a successful push or need to defend a lane. People should definitely utilize them more, because I'm usually the only one glowing sometimes.

I buy a blue elixir(for mages) and red/green for DPSs after I get my third item, and from then on I buy them occasionally. When I have all six items I just spam all of elixirs.

My favorite/most used strat at the moment is to go AD Ezreal solo mid and start with an elixir of fort and 5 hp potions. Cleanse ignite for summoner skills and I wreck any opposing lane. It gives me complete dominance over the lane and makes last hitting the easiest thing ever. Not to mention I get FB 50% of the time (the other 50% is about 40% getting them to go back to base with really low hp and I push the tower/ 10% is they survived with 1/4 hp, use hp potion and play defensively and I can exp deny them).

I usually get 1-2 before teamfights, baron or pushes. When I play Kayle I get Rageblade then triple-elixir and just destroy everything.

If you don't use elixirs you are doing it wrong.