I would clean off the chrome bars that the head slides back and forth on. Clean with alcohol and then put a small drop of 3 in 1 oil on the bars. These are brass bushings, so keeping the bars clean and lightly lubed is important. If this is an old plotter, they could be worn and would also contribute to this kind of poor plotting.
In the software, make sure that you're sending as a pen plot if you're using Omega to send the jobs. Tangential mode won't affect pen plots other than to slow it down and swivel mode will put hooks on the corners.
Good Luck