Will visiting the radiation oncology department expose me to some amount of radiation?

No! There is lots of shielding around all the machines, so there is no risk to casual visitors.
No. Radiation oncology centers are very well shielded. In fact, the amount of radiation exposure is less than walking around outside or flying in a plane.
Likely Not. There is background radiation in the environment. If you stay out of the required well labeled restricted areas, it is unlikely you will be exposed to any or at least any relevant amount of radiation.
No. Not unless you are a patient being treated or someone who works in the department handling radioactive sources.