Kiwi back rower Anderson has signed a two-year extension while Wood and Hicks have agreed one-year deals.
Head of Coaching and Rugby Tony Smith said: “I am delighted with each of the boys who have extended their contracts. It shows the faith they have in the club and its future, which is what we are building towards. Each of the players deserves to be here with their solid performances and support of club. I look forward to working alongside them in the future.”
Prop forward Wood is a product of the Wolves academy system after joining the club in 1999.