Regarding Biden, I have random back issues of the Almanac of American Politics. In those, they quote National Journal's rankings of the sitting senators. They break it down by economic/cultural/foreign, but I'm just going to take a rough average between the three categories.
In Senate votes during the 2000 calendar year, Biden was more liberal than roughly 77% of his fellow senators.
In 1995, it was 65%.
In 1982, it was 75%.
To put things in perspective, the following Democrats in 1982 tended to be below 50%:
Howell Heflin, Dennis DeConcini, Russell Long, Bennett Johnston, John Stennis, Edward Zorinsky, James Exon, and Lloyd Bentsen.
The following Republicans tended to be above 50%:
Lowell Weicker, Charles Percy, Charles Mathias, David Durenberger, John Danforth, Mark Hatfield, Bob Packwood, John Heinz, Arlen Specter, John Chafee, Robert Stafford, and Slade Gorton.
No scores were given to senators who were not reelected that fall.