Is there any difference in the meaning of these words? Which one of them is used the most in everyday conversation?
In my vocabulary for both words I've found essentially the same meaning: "difficult to do and needing a lot of effort".
To me the difference lies in their origins.
"Onerous" means "burdensome" - not necessarily difficult or physically hard, but unwelcome and required of one. (Maybe unpleasant, or just taking time away from other things)
"Arduous" means "requiring effort".
These may overlap in many cases, but to me are quite different.
I would say that "onerous" implies more of a mental difficulty, while "arduous" is a physical difficulty.
That contract placed an onerous duty on me because I had to tabulate the reports every day.
Moving the furniture upstairs was an arduous labour.
However, the distinction is usually fairly transparent in context, so you can generally use either word without loss of meaning.
Onerous means "burdensome", related to onus "burden". Arduous means "difficult" and derives from the Latin arduus "high, steep". So while there is certainly some overlap, the words are not perfect synonyms. For example, it would be appropriate to refer to:
...the onerous backpack on our arduous climb...
or, in a figurative sense,
...the onerous secret in our arduous relationship...
It would make less sense to talk about "the arduous backpack on our onerous climb" or "the arduous secret in our onerous relationship".