Well, a blanket statement like "No such thing as over-oxygenating" just isn't true. Because it is possible. Just incredibly unlikely in a home aquarium.
In fact, an oxygen saturation of 105% is deadly for fish. But, like I said, it is practically impossible to do this at home.
The important concept here is one of equilibrium. The system, in this case the oxygen in the air and the oxygen in the water, will always tend toward the equilibrium point. Equilibrium is achieved when the sources and sinks of oxygen are balanced. The sources being oxygen from the air, and the sinks are the plants during the night and the fish. When these are in balance, the water holds a certain amount, called the equilibrium concentration or equilibrium point. Whenever the system is not at equilibrium, it will always tend toward equilibrium.
For example, if your water held less oxygen than the equilibrium point, oxygen would enter the water through the air-water interface until equilibrium was reached.
Now, another important fact is that this equilibrium point is temperature sensitive. Fish respire at different rates depending upon the temperature, and the water holds different amount of gases depending upon the temperature. And, liquid dissolves less gas as the liquid's temperature increases.
In this way, cool water at 100% equilibrium, if heated up quickly, could get to 105% equilibrium, the deadly point for fish.
The reason I say it is unlikely, is that oxygen transport at the surface is relatively rapid, especially with a filter return or air pump. It is very difficult to heat the water up quickly enough without allowing the re-equilibration that occurs.
This is why it is pretty much impossible to over-oxygenate your water in a home setting. You could even bubble pure oxygen into your tank, and it would not make a difference. The system always tends toward 100% equilibrium.
All that said, the lesson here is that that LFS is rather untrustworthy. And, the above posters are definately right. Both the ammonia and nitrite are at very dangerous levels. To help, immediately do a water change. Then, several hours later, do another one. In fact, so long as the temperature and hardness and pH of the replacement water is pretty close to tank water, you can do as large a % water change as you can handle, even 80-90%. Obviously one 80% water change lowers those 5.0's to 1.0's, a vast improvement. Or you could achieve roughly an 80% drop with 5 20% water changes. To be really safe, you need to keep doing waterchanges every few hours or at the minimum every day until the levels are at least as low as 1.0 ppm each. That is still not safe, as the levels need to be 0.0 in the long-term, but under 1.0 at least gives your fish a chance. Clean water = healthy fish, and lowering the pollution levels in your tank can only help increase the chances of your fish survivng pop-eye.