Head coach Richard Hill was recently given the go-ahead by the club's board to begin contract negotiations with 10 players whose current deals expire at the end of the season.
Fly-half Strange, the joint leading points scorer in the Guinness Premiership, turned down other opportunities to remain at the Memorial Ground for another two years.
Cox is also committed to Bristol until 2008 and Nicholls has put his medical studies on hold again to agree a one-season extension.
Bristol made a confident start on their return to the top flight - four victories from nine games puts them in eighth place - and Strange is determined to keep the club in the Premiership.
"I'm really happy here at the club, both on the pitch but also with the coaching side of things," he said.
"Richard has assembled a great squad and it's good to be part of it. There was interest from one or two other sources but, once Bristol made it clear that they wanted me to stay, it was a simple choice.
"There's a tremendous spirit on and off the field and I'm really looking forward to the rest of the season and doing my best to make sure that we're playing in the Premiership for the rest of my contract."
Hill hopes to tie down the remaining deals in the next weeks and he is also looking to secure loan moves for four of his squad - props Martin Ropside and Jason Hobson, number eight Richard Martin-Redman and centre Andrew Reay - while the Guinness A League takes a break.