If Scott stole the camel, he was lying and Tommy did not steal the donkey. But in that case he would have stolen the horse, and have told the truth - but he could not have, since he claimed he stole neither horse nor donkey.
If Tommy stole the camel, he was lying; however, since he claimed to have stolen neither the horse nor the donkey, he would have been telling the truth.
If Robert stole the camel, he was lying and Tommy did not steal the horse. But in that case he could still have stolen the donkey, with Scott stealing the horse and telling the truth.
Conclusion: Robert took the camel, Tommy stole the donkey and Scott made off with the horse.