Hello Red Fish.
Thanks for that question.
It is not possible to install Exodus on a USB. Exodus needs to be installed on your computer. But even if you could, that wouldn't offer any protection I'm afraid. If your computer was infected with malware, let's say one that can read your memory, then as soon as you connected the USB and opened Exodus, your Private Keys would be loaded in memory and they would be compromised.
But if you're worried what happens when Exodus is closed, let me put your mind at ease by saying that if you have done the backup process and used a strong password then your Private Keys are encrypted and that encryption is virtually impossible to break. In fact it would require Terrabytes of RAM to pull off such a feat, and even then it's not certain.
So, the best way to keep your funds safe when using a software wallet, is to keep you computer clean and never share your private information with anybody! And, of course, there's always the solution of hardware wallets where the Private Keys never come in contact with the outside world and that's why they're considered the safest method of storage. It's what we suggest for large amounts of money.
Let me share a few articles with information on the matter:
https://support.exodus.io/article/145-safety-and-security-tips
https://support.exodus.io/article/45-can-exodus-safely-store-large-amounts
https://medium.com/exodus-movement/the-dos-and-don-ts-of-12-word-phrases-and-private-keys-89f6c800eaec
https://medium.com/exodus-movement/addressing-vulnerabilities-with-software-based-wallets-1cc9ff77bf44
I hope this helps!
Michalis