I read that there are three lame duck senate races (senators that will start their term right after the election and not in January). Is that right? Illinois is one, what are the others? Why would they start then and when would they be sworn in?
Is it possible that dems would get a 61st seat, temporarily, this way and use it to change some senate rules?
The reason they are seated immediately (or at least as soon as the election is certified to the Senate and the Senate swears them in) is because they are filling an unexpired term for senate seats which are were previously vacated for one reason or other: West Virginia, Robert Byrd dying , Illinois, Barrack Obama resigning to become President, (don’t know what the third one is), and the governor of those states temporarily appointed a replacement until a permanent one could be elected. The only reason most other senators must wait until Jan 3rd is that their terms to which they are elected do not begin until then; the replacement senators are elected to terms that are currently ongoing and therefore can be sworn in at anytime.
Illinois is kind of an interesting case in that the replacement election is for the remainder of Obama’s term, which expires Jan 3rd (two months after the election), and a separate election is taking place for the term starting Jan 3rd, 2011; although I believe the same candidates are running for both elections on the Nov 2nd ballot.
As for the Dems getting a temporary super-majority , no, at least 2 of those 3 seats are already held by Dems (Rolland Burris and Byrd’s replacement). In any case, 2/3rds of the Senate (67 votes) are required to change the rules, not 60 (60 votes , or 3/5ths of the Senate, are necessary to break filibusters, not 61).
Always thought a lame duck was a politician who is not returning for a new term post election.
Illinois has separate elections to fill Burris’ (ne Obama’s) seat for the lame duck Congress and for the new full term beginning in January, 2011. This is the only one (as far as I know) that fits the OP’s description, and - yes - all the candidates in each election are the same, and it would be amusing as hell if different candidates won the separate elections. At least the short-timer could put “United States Senator” on his tombstone. 
West Virginia is a straight special election to fill the remainder of Byrd’s term, which does not expire until January, 2013. I assume the winner would take office immediately, but wouldn’t be a lame duck.
I can’t think of any others off the top of my head, either.