Have you tried using a clean brush rather than a Q-tip? "Dry" oil paint can still be manipulated and really should be varnished over in order to protect it once you have finished painting. Clean up should also be done, wherever possible, at the time of painting so you don't have to keep adding thinner to the model and potentially eat through to lower levels of paint.
Also make sure you varnish the model before you use oils on it to give some added protection.
Edit: We do have an
oil paint article - I've not added anything regards cleaning up so please feel free to add anything you feel might be useful (ie potential problems, ways round them, etc).