Is there a way that my iMessages can be going to a device that is not signed in to my Apple ID? I've been made aware that my iMessages have been going to an iPad that I lent to someone a while back. I do not want this particular person to have access to my messages for several reasons. They are refusing to return it to me so that I can fix this issue. 

I tried to locate the iPad on 'Find my iPhone' so that I could remotely wipe it but it is not on my list of devices. I am fairly sure I had signed out of the Apple ID before lending it out. I have changed my AppleID password in the case that the iPad is still signed on. But beyond that, I am not sure why the iPad was receiving my messages or how else I can stop it. Is it possible the messages were going to my device without the AppleID? How can I stop the messages without having the device in my possession? Appreciate any feedback, thank you.
There are multiple places in which your AppleID can be used on a given device: iMessages, FaceTime, iCloud, App Store, etc. It sounds like what is going on is that the iPad is still logged into your AppleID for iMessages, but perhaps not for other items.

Perhaps the easiest way to handle this is to change your AppleID password. You can do this on Apple's site: https://appleid.apple.com. After that is done, you will then need to go through each of your devices and update the password that is used for the App Store and Messages/FaceTime.