I have a list with two content-types. I only want the user to be able to edit or delete listitems created from only one of the content types in SharePoint 2013.
Permissions are on the items themselves, not the content type. However, you could fake it by making custom New and Edit forms for the read-only content types that either redirect to the Display form or simply render the same read-only controls as the Display form. This isn’t true security as the user, technically, still has write access to the list.
Marta’s suggestion about an event receiver is the truly secure option. You could also add some security-checking code in the code-behind for the custom forms I mentioned above. These options require custom development, and they may not be available for use on SharePoint Online.
Another option would be to use workflow in place of the New/Edit forms on that list. You would need to modify the content types’ schemas to disable New and Edit forms. You would also need to modify the UI to provide users a convenient way to start the workflow. Workflow doesn’t happen as immediately as the New/Edit forms, so you would need to either provide additional UI/code to make that flow properly or train users on it. This is certainly a complex undertaking, but it can be done with some PowerShell and SPD.