First, you will during the process of reinstalling the carpet cut your fingers on the tacks. If they are rusted and with cat urine, you could be asking for trouble.
But, then, you would have to reinstall new tack strips, so I would elect to use the rusted ones. If your carpet is lighter than rust, you migh develope stains from the rust in the near future.
Anyway the "how to" on the carpet strips.
The tacks should be leaning to the wall area. The tacks are to catch the under lining of the carpet and hold it in place when you do the stretching. Your carpet must be stretched during this process either by you with a knee kicker or by a professional.
anyway, grab about one inch of carpet on the tacks and then with a putty knife cram the remainder of the carpet down between the tack strip and the wall/floor molding. The tacks hold the carpet in place, and the forcing of the carpet down under the molding holds it more in place by being over and below the tack strip.
Do one side at a time then stretch the opposite side. Then attach the other side, then stretch its opposite side. Really your stretching only two sides. One side is manually attached to the strip then its opposing side is stretched.
Be careful not to drag or tear the carpet under lining. If you do, the tacks will have nothing to hold on to. Some times this happens on carpet taken up too many times.
Before you tack down the carpet, you should pour a box or more of baking soda between the pad and the concrete flooring to just soak up odors and the ones to come. Won't hurt any thing.