All of my quests are higher level than me, what's a good way to catch up?

There are most likely some places(Quest Hubs, Area Bosses, Dungeons) that you have not been to yet. If you look at the image below, you will see that there are a ton of white markers and a few black markers. The white ones are places that I've been and completed all of the quests/tasks. When you look at your map, do you see any black markers? If so, head over to them and you will most likely find some new quests to complete.

Dark Anchors/Dolmens, area bosses, public dungeons all reward you with a decent amount of experience the first time you complete them. You will have to explore to find these places and then they will stay on your map. If you compare the image above with the image below, you will notice that there are a few area bosses that I haven't even discovered yet as well as a few other places. The map below is from ESO Head's Interactive Map. If you're having trouble discovering the places you've missed, this is a very good site for finding them.

Make sure you've completed all of the guild quests and the main story quests that are available to you.

There are also 3 dungeons per an area. Even though two of them are located in the the opposing alliances' area, you may join a group and travel to them from a wayshrine.

You usually get left behind if you skip or miss some of the content. The funny part is, if you do it all, you usually get too far ahead.