This question arises when I try to describe my itinerary to ticket service in the UK. Take for example, I plan to buy a ticket from A to B. B is the terminal. How to say its counter part A? I cannot find a proper term. I have to say "I will depart from A" or "I plan to go to B from A". Or I even use "departure place" to refer to B.
Terminal is not commonly used in the sense you describe. If you buy a ticket from point A to point B, point A is your origin and point B is your destination.
On a fixed route such as a railroad, each end of the line is known as the terminus; while this word refers to a final end point, which point is the start and which is the end obviously depends on your direction of travel. Terminal, on the other hand, usually refers to the building or other facilities where travel begins and ends.
I too would find origin confusing in this context. "What is/was your origin?" could mean many things, such as your ethnic origin, place of birth, etc.. The meaning "Where did you start your journey?" would not be a meaning that would normally occur to me on hearing "What is/was your origin?".
Personally, I would use starting point, departure point, or something similar.