I recommend JuiceSSH if you happen to use an Android phone. It's by far the best SSH client for Android I have seen and supports login via password as well as login via private key authorization.
Using different SSH keys for different devices has the disadvantage that you have to handle different keys but the advantage that should one of the devices get compromised, you can just delete that one corresponding pubic key from the server and don't have to hustle to create a new private key on a different device asap and switch the public keys out. So I'd recommend to use different keys for different devices but that's of course personal choice.
You might not be able to create SSH keys inside an app. In this case, create more keys on your computer and transfer them to your mobile devices. To create them, simply run:
ssh-keygen -t rsa -b 4096 -C "yourEmailAddress@host.com"
To make your server accept connections using different private keys, append the file
~/.ssh/authorized_keys on the server with the public key. The default location for the public key of your first key pair is
~/.ssh/id_rsa.pub on your local machine.