Can my messages be synced when I sign in on another iOS device? I have an iPhone and an iPod and I was using the same Apple ID on both devices but I changed my password on my iPhone. If I sign in on my iPod, will my messages from my iPhone be synced to my iPod?
If you change your Apple ID password, all instances where it was used should prompt you to update it before using it.
So after changing your password, your iPhone iMessages won't be synced to your iPod.

From the Apple Support page:


  The next time you use Apple features and services that require an Apple ID, you’ll be asked to sign in with your new Apple ID password.


And here:


  By changing your Apple ID password you can prevent anyone from accessing your iCloud data or using other services (such as iMessage or iTunes) from your missing device.


After you sign in again on your iPod, all new messages should be in sync, but in my experience it won't sync the messages in between the password change and the sign-in.