cleaning staff

They're usually called cleaners here in Australia, but cleaning staff doesn't sound odd.

"Cleaning staff" is a formal, official way of referring to employees who perform cleaning duties. It is how they may be described in recruitment advertisements, internal company documents, employment contracts, etc. "Cleaners" is much less formal and is more likely to be used verbally in everyday speech by the occupants of the building which is cleaned. The workers themselves may well prefer the more formal title and see it as more dignified.

There's nothing wrong with "cleaning staff" or "cleaners." However, In the US, the word "cleaners" often refers to dry cleaners, not people who do cleaning chores. People who are paid to perform cleaning chores are often called janitors.

Yes. This seems to be a British English (England, Scotland, Wales, Ireland, Australia, New Zealand, etc) versus US English difference. I am not sure about Canada - I see they use janitor, caretaker, custodian, and "light duty cleaner" in job advertisements.

Although British English speakers don't usually call cleaning staff "janitors" there is a category we see in office supplies catalogues "catalogs") sometimes called "cleaning supplies", sometimes called "janitorial supplies" - mops, buckets, disinfectant, air freshener, cleaning chemicals, paper towels, toilet paper, soap, etc.