The tie rods, centre (drag) link, and idler arm are the steering components. The car must be aligned after you changed the tie rods. Changing all these will reduce the play on your steering wheel (assuming there is play right now) but it will probably not solve your shaking problem.
Your shaking problem is probably tire related. Since your tires are quite worn, it is probably time for new tires. When you install your new tires, have the shop check the wheels for trueness. Good luck.