Why would overemployment mean that labor is used inefficiently? If labor is being used efficiently, there is no excess unemployment
  or over employment.


This phrase from Khan Academy struck me as quite strange. Why on Earth would over employment mean that labor is NOT used efficiently? Labor is a resource. And if we can use more of a resource without increasing its size, then it would seem that we are using it more efficiently, we are using bigger share of it.

For an example, land is recourse. If we will drain swamps we will be able to use more of land for commerical purposes, meaning that we will use land more efficiently. I believe that similiar reasoning can be applied to labor.

P.S. What I understood from comments: Overemployment is inefficient because it happens due to sticky wages/prices in short run equalibrium. Sticky prices/wages create inefficiency in the market, thus it should be nothing suprising that overemployment caused by sticky wages/prices leads to inefficient use of labor.
Because using efficiently does not mean that all labor is used (this holds also for any other factor of production). This is so because on the margin at some point additional inputs might not produce enough value to justify the cost.

Consider simple supply and demand on perfectly competitive labor market with no market failures and all standard background assumptions.

Supply is: $S_L=10+w$ where $w$ is wage. Also let’s suppose there are enough people so that maximum 100 labor hours ($S_L \leq 100$) could be supplied after that there simply is no more labor hours due to lack of people.

Demand for labor hours is: $D_L=100-w$.

Now given the supply and demand it’s trivial to calculate that equilibrium wage is $w=45$ and equilibrium employment will be: $S_L=D_L=55$.

This equilibrium is completely efficient yet only 55 hours of labor is demanded. Employing 60 or 70 or 100 hours of labor would just reduce total welfare as measured by total surplus, and hence it would be inefficient. 

Intuition is that because given the firms demand which is derived based on their own optimal production decisions given the prices they face for their product the equilibrium wage is too high to justify employing everyone. Employing more than 55h of labor would start destroying value as those workers would have to be applied to activities where simply the value of output is not sufficient to cover the cost of that labor. Of course, there could be situations where all labors would be employed if equilibrium demand is equal to maximum number of labor hours there is or exceeds it.