"at odds" means "disagreed with." In this case, it's reasonable to assume that the boss disagreed with/had a problem with the new employee's qualifications and ability to perform his job well.
Honestly, it's not a perfect answer. "At odds" suggests some sort of conflict and that isn't evident from the rest of the statement. However, it's easy to rule out the other two options.
"at a loose end" isn't even the usual construction; it's usually "at loose ends." And it suggests confusion or an unresolved situation. Further, the question states that there are multiple issues--qualifications and the ability to perform the job. "at a loose end," at best, would mean one area of disagreement, not multiple areas.
"at a standstill" doesn't work, either. "At a standstill" suggests a deadlock or an irreconcilable problem. While we know that the boss and the new employee disagree, not all disagreements end up as deadlocks. In fact, most disagreements are resolved.