None of them is common. A BNC search for
Code:
[work] on|at|with a|the|my|your|his computer
gives a total of 8 results, of which the directly relevant ones are:
- She said she slept in it because she worked on a computer that was only available to her at night and there was no point in going...
- In other words, no one working with a computer should be forced into a straightjacket of usage...
- ...he said it was not viable to work on a computer of that age and invest in a new one...
- ...something which is particularly important for health reasons if you work at a computer.
Not really enough data to draw any definite conclusions.
COCA has considerably more results (perhaps because it uses more recent texts), and seems to favour
on,
at,
with in that order.
There are additional complications. For example, the noted computer algebraicist Doron Zeilberger would say "with" because he anthropomorphises his computer (going to the extent of listing it as a co-author on his papers).