Here is a reply I got from Exodus support regarding EOS:
As for EOS, At the moment, doing this in Exodus isn't supported. However, we may come up with a method within Exodus which will register your EOS for you automatically in the future.
I strongly advise waiting, because the process of EOS registration is complicated, and requires exporting your private keys. Exporting of private keys is something I do not advise doing because of the huge security risk it creates!
If you don't want to wait for a potential solution in Exodus, and want to take the risk anyway, here is what to do:
You have to export your Ethereum private key and import it into MyEtherWallet.
Here's how: h t t p s : / / v i m e o . c o m / 2 2 4 6 8 0 9 9 4
Spaces between characters in Vimeo link added intentionally
Once again, please be very careful with your private key. Anyone who gets it will get access to all your ETH and ETH (ERC20) based tokens!
Here's a step by step guide to help you register your tokens:
http://support.exodus.io/article/65-i-ve-received-eos-tokens-in-exodus-how-do-i-register-them
When you receive EOS from the ICO, you should use MyEtherWallet as well. Once they are delivered, you can transfer them into Exodus for safe keeping or exchange.
I've been holding off registering hoping that Exodus will take care of it for me.
They may, but I didn't want to even have to worry about having to do it anymore. Relying on others can be stressful at times. I prefer handling business.