The tie rods (more specifically the tie rod ends) are the only things that control the alignment on the tractor. Yes, they can bend easily, especially on the cheapo 1000 series tractors like the 1554. They are quite flimsy. There is no stabilizer. It's also quite easy to bend a spindle or even bend the axle, and this happens often if you've hit a hole in the yard or a tree. Could be a combination of things. Unfortunately, you'll probably have to disassemble the front end, and look for a bent or broken piece. Things should look uniform (left to right) but the only way to know may be buying a new tie rod to see what it is supposed to look like. This is what a dealer would do, only charge you $50 an hour for labor.
Also, double check the front wheel bushings. There are no bearings in 1000 series tractor front wheels, they are just nylon bushings. Those obviously are easy to wear out and could give you the same condition. I'd start by jacking up the front end and looking for play in the wheels themselves.
1951 Farmall Cub, Cub Cadets 102, 104, 1811, 1864, Simplicity Legacy XL 4x4 Diesel with FEL, 60" mower, 50" Tiller