Ehrhoff scored eight goals and had 34 assists in 77 games last season. Lukowich, a native of Cranbrook, B.C., had eight assists in 58 games.
"We are pleased to be adding Christian and Brad to our defensive group," Canucks general manager Mike Gillis said in a statement. "Defence has been an area we wanted to add skill and depth to and this trade has strengthened our group considerably."
Rahimi scored one goal and had five assists with the Canucks' AHL affiliate in Manitoba last season. White, drafted in 2007 by Vancouver, scored seven goals and had nine assists with the University of Minnesota.
The addition of Ehrhoff and Lukowich will help shore up Vancouver's back end after longtime Canucks defenceman Mattias Ohlund signed a seven-year free-agent deal with Tampa Bay in July.
The deal allows the Sharks to clear plenty of space under the cap.
Lukowich, in the final year of his contract, will be paid $1.8 million.
"This trade speaks to the confidence we have in the young players coming up through our system who have earned the right to compete for a spot on this team," Sharks GM Doug Wilson said in a statement.
"It also creates some flexibility in our team payroll for potential future transactions as the season progresses and adds two more talented players to our reserve list that can help this organization in the future."