So there are like 900 different currencies and items groups you trade in for things it seems?
There are various event "currencies" but they are not tradeable. Though you can use them to purchase things from various vendors yes. There aren't all that many, about 10 or so total.
Eternity Splinters are the in game currency that you can use to buy heros, ultimate upgrades, team-ups, aka most of the things you would otherwise pay cash for. They have an internal timer of 7 minutes and drop fairly shortly after that timer is up each time, faster if you have higher special item find
Odin Marks are quest reward currency granted from Legendary Quests (available starting at level 20, and also the fastest way to level), Shared Quests, and some other special items/events. They are used to buy Legendary slot items and to bless artifacts (blessings can be traded by blessing an artifact and then trading the artifact. You can then use the crafter to swap the blessing to an artifact of your choice)
Eyes/Hearts of Demonfire are Shared Quest rewards and Raid rewards. They are used to buy upgrades for uniques and cosmic items and to grant Stat bonuses to slot 1-5 gear.
Other than that most of the other currencies are event specific, right now you'll get a few different kinds because you started playing during arguably their best event ever which combines 8 other events into one. Those can be traded in at event specific vendors for rewards.
People really only trade via items. They use actual item drops as currencies (ala SoJs in D2). The big three are blessings (purchased with Odin Marks), Loki runes and Gem of the Kursed artifacts (abbreviated GoK). But it's a pretty true bartering system so anything worth something can be used to trade.
As an aside, you should know you have to level up your vendors by donating items to them. The first vendors you should level are the Crafter and the Asgardian Enchanter. You take slot 1-5 items from your inventory and alt+click (I think it's alt+click) to donate it to the vendor who's window you currently have open. This is what you should be doing with all your sellable items until they are maxed.