I've recently been terminated from my job,(though the words "terminated" or "fired" have yet to be uttered from anyone's lips. What I have been told, is "your job will be advertised, and we are giving you some time to find a new job".
Well, it sounds good to give me time, but I work over 40 hours a week, and am not at all sure when this "LOOKING" will take place, especially since those words have yet to be uttered.
I've asked my HR director, if my accrued vacation and sick time can be used after I am replaced, and he didn't know! He said he would "research" it, but it seems, I am doing his job also.

Any ideas???

Your employer is required to pay you for any vacation earned, but not sick time usually, sometimes it depends on which state you work in.