I was have wallet on etherdelta, with etherdelta generated address, but now my account just dissapeared on that exchange. Anyway, I can see my account on etherscan, with my corect balans-tokens (aion). Now, how can I send that aion tokens from my address which I can see on Etherscan, directly to my My Ether Wallet ?
When you created an account on EtherDelta, it generated a public address and a private key, and prompted you to save the private key. If you did not save it, you might be in trouble.
If you did save that private key, then you can get get access to your tokens by importing that private key into an ETH wallet. The simplest one would be Metamask - it's a Chrome browser extension that works as a bridge to the ETh network. After you install it and agree to terms and conditions, you can click on the menu at the top right corner and select Import Account. Paste your private key there and voila - you have control over your account again.
Please note, that Metamask by default only shows the amount of ETH that you have on your address. To you see your tokens, you need to add token contract address of that token by clicking Add Token on Tokens tab in Metamask.
As you can see on etherscan.io, AION contract address is
0x4CEdA7906a5Ed2179785Cd3A40A69ee8bc99C466, so click Add Token, enter this address, then switch the tabs and switch back to Tokens tab and you will see your AION balance.