Why Janna? What makes her a strong presence?
She was one of the top supports in season 1.
She's also maintained about a 55% win-rate for ~3-ish years in a row? Probably more, and she's reliably been in the top 3 for years. Last worlds she also happened to get an 85% win-rate, and a 90% win rate for the qualifiers. She's historically had the single strongest showing of any champion over LoL's history, despite multiple nerfs. It's extremely unlikely Riot will nerf her in any significant way to oust her from being extremely reliable, especially because you will never, ever find a Janna QQ thread from salty players.
The why her prescience is strong is mostly she's just really good at what she does.
The general strength of a (ranged) support is counter-initiating and peeling for their carry, and Janna is extreemly solid at both.
Janna also gives a +50 AD steroid by slapping shields on people, so marksman tend to waltz around with an extra ruby crystal and B.F.Sword when Janna's on their side.
Why orianna over annie?
Ori has a lot of pros relative to her cons. She's pretty much a Jill-of-all-trades with solid utility, range, CC, early, mid, and late-game prescience.
Ori's only real weakness (at least compared to other mages) is her damage is a little low and her skillcap is pretty unforgiving.
Her CS potential is so godlike the damage bit doesn't really count for anything if you can master her though, ditto for skillcap.
Annie's a solid champion - but she has a lot of clear cons. Her (ability) range is about as short as it gets for a ranged champ, and her stun is extremely predictable and easy to play around. With how Annie's stun operate, it tends to force 1v1 lanning into a position where you can hold onto the stun but sacrifice CS/wave control, or you sacrifice having a stun for engages in favor of CS/wave-control.
Jarvan seems to get banned in most ranked games I play, what would you recommend instead of him?
's pretty solid.
Is rumble and jax really that powerful?
They aren't that powerful, it's more top-lane is extremely turbulent and 
is the only champion that really maintained being a strong pick for an extended period of time.
Counter-picking is more important in top lane than most, which is why it's generally pretty turbulent.
Jax and Rumble are just reliable and haven't been victim to the same kind of king for a day -> not optimal spike most top-lane champions fall into.
Partially due to their strengths against counter-picking. Rumble is a lane bully that will just usually have an edge, Jax is weak early but niegh-impossible to counterbuild, so if you can just play to his strengths and survive early he's pretty reliable.
What would you recommend for a fast route to 30?
Sub-30 summoner levels?
Depends on what question you answered for your account. If you answered as having lots of MOBA experience, you're going to fight nothing but smurfs and alt-accounts, so just stick with the 10 champions you're picking out.
If you answered no MOBA experience - champions in LoL are balanced around their capacity to blow up the Nexus, and balance assumes a certain level of mistakes and competency. Ranked Bronze though Diamond win-rates don't really differ, so the level 30 with 10 champs and decent rune pages ranked mindset.
Champions aren't balanced around their 1v1 potential, snowball potential, or around the level of mistakes/lack of visibility you'll run into with inexperienced players.
Fighter/Assassins are really strong in 1v1 situations, snowball really hard, and focus on exploiting mistakes.
