Removing motion path from object states

It sounds like a character with a motion path was copied and then pasted directly into the custom states.

I've seen issues where an object with triggers was pasted into a state. After that's done, there's no way to delete those triggers, which messes up other programming.

The solution to that trigger issue—which might also work for this motion-path issue—is to delete the pasted objects from the states. Then insert new ones (after ensuring that they don't have any triggers or motion-paths). 

If that's not the problem, you could contact support or upload the file here, as Ange suggested. Here are the best practices for uploading a .story file:

• Only include slides that are related to the problem.
• Be sure objects, layers, motion paths, and variables have meaningful names.
• If there is proprietary content, replace or delete it. For example, replace proprietary text with “ipsum lorem” text.

BTW, when you're changing the state of a character, there's no need to copy and paste copies into different states. Just add a new state to the character, then change to a different pose while editing the new state.