I wonder whether the meaning of "travel company", "travel firm" and "travel agency" is the same. Can we use them interchangeably to vary the language in a paragraph?
While Radu Miron's answer isn't incorrect per se, in a general context, the terms in your example are entirely interchangeable. You could also add "travel bureau", or "travel organisation" if you need more.
However, if your paragraph is discussing or explaining different types of companies that assist travellers (assuming there is a range of types of travel company), then you would need to be careful about which company type you used where. It all depends on the context.
Incidentally, as inferred by Radu Miron, travel agency is probably the most precise of the choices as they act as an intermediary between clients. You could also use "travel agent"/"travel agents" without loss of clarity - even though this would, strictly speaking, refer to a person/people rather than a company.