Elyos Leveling Guide 18 - 20
Once you reach the Veteron Obeservatory grab all of the quests and update your Campaign "Nest of Lepharists" quest. You will be turned into a bird and required to fly northeast to the Mysterios Shipwreck. Video of exactly where you need to go for the Nest of Lepharists quest.
After you explore the Shipwreck return to town and update your quests. Before leaving town, bind at the Obelisk. First quest you will want to do is "Flotsam". This quest requires you to smash 12 of the Abandoned Cargo crates around town.
After you've destroyed all 12 of the crates you will want to kill 12 of the Sea Starturtles in the area. They can be found practically every where. While you're killing them you'll also want to collect 
15 Venera. Chances are your skill won't be high enough, don't worry about it. It doesn't give good XP anyway.
After you're done both "Flotsam" and "Saving the Snappers" return to town and turn in both of your quests. After you've done that head back towards the Mysterious Ship that you had to explore earlier.
Here you will need to kill the Lepharist Revolutionaries until you get the clue that they drop. You will be here awhile, the best thing to do is get a group together which will not only get you good XP, speed up your kills so you get the drop sooner.... You will also be able to complete the "A Nest of Lepharists" quest.
Etheir way, once you kill enough of the Lepharist's to get the 
Lepharists' Order return to town and turn in your quest. Now, to do a belated quest. Around the Observatory you will find Sand Potcrabs.
You'll want to kill the Potcrabs for 
7 Sharp Pincers. Once you have all 7 Sharp Pincers you will want to return to town and turn in your quest. Now you have two options to get from level 18 to 20.
Your only options to get from 18 to 20 is completing the group quests at the Tursin Outpost or grinding. The group quests will be much much faster, however if you can't find a group your best alternative is to grind out the levels. Luckily grinding is pretty much as quick as questing if not faster. If I had to choose a good spot to grind it would be where you killed the ghosts for the quest earlier.
NOTE: If you're able to handle mobs 1 - 3 levels above your level I recommend going to Theobomos at level 19 or even 18. You'll get better XP and be able to get out of this area sooner.
This area has pretty weak mobs, which will allow you to kill quickly and also they are still within a half way decent level range. As far as the elite city goes I'm not going to bother listing a strategy for it and a guide. In order to do it you will need a group and chances are someone in that group will know what to do.
When you reach level 20 you'll want to head back to Verteron Citadel and Teleport to Theobomos.