Yes you can trade on EtherDelta without any verification and they have most of the ERC20 tokens too (they may not have em all). All you need to do is go to the top right corner hit "select account" > "new account". Make sure to back up your private keys though when you hit "forget account" it will show your address and your private keys. It is critical to back those up so you can regain access back into that account.