Are oaths prohibited or only discouraged?
And is there a difference between swearing what happened in the past versus swearing what one will do in the future. One can't be sure he will live up to his oath to do something in the future, but at least on things one can actually remember, that can't get him into trouble, he ought to be able to remember much of the past (and when he can't, for example as a witness in court, he can just say he can't remember.)
Let's call it "very strongly discouraged." If they were all-out prohibited, the Torah wouldn't have a procedure for them.
There was a point when Jewish law would demand an oath in financial proceedings (e.g. "I was supposed to watch your cow and I swear I didn't abuse it in any way, it was hit by a lightning bolt"), but we try to avoid those today whenever possible. An oath for the future (e.g. the fellow swearing to avoid ice cream or the like) is occasionally done by some, but often inadvisable as well.
In today's US courts, Jews prefer the option to "affirm", rather than "swear." It has the exact same US legal implication (you can be found guilty of perjury for knowingly making a false statement), but we believe it's less demanding from a religious perspective (the Talmud has stories of God punishing people for minor misstatements when under a religious oath).
