How can I get odors out of concrete?

There is something on the market called muractic acid. It is very toxic and you need to use gloves, goggles and a respirator to use it. All you do is pour it on and let it do its work. But first you might want to pressure washer this and use a concrete cleaner that is concentrate. Then use the acid if this doesn't do the trick. You will have clean looking concrete and hopefully the smell will be gone to.

Actually a quick and environmentally safe way would be to use a spray can of Shellac. It will seal the odor in, and it non-toxic. In fact the stuff is used on a lot of candies for the shell. As to the staining part this will not work and many of the other answers will do such as bleach.

Well, I'm not sure about the extremely strong odors your talking about, but when I rented a home, the people that lived in before ate a lot of curry. I used vanilla extract in the paint to put onto the wall and ceilings and the strong vanilla scent over power the other. I'm not sure about getting rid of rat smell.

To eliminate the odor and keep it gone for good you'll need to use bleach and a power washer .(you can rent one if you don't have one) but if that's not an option using bleach and water and a good stiff push broom will do the job (just more work).Then applying an odor blocking primer should be all you need

Baking soda and hydrogen peroxide and a small amount of dish soap. Make a syrup and spread it around. Let it stand over night and then mop it up with a weak solution of pine-sol and water. Should do the trick.