Place black-eyed peas into a large container and cover with several inches of cool water; let stand 8 hours to overnight.
Drain and rinse.
In a large pot, cover black-eyed peas with fresh water. Bring to a boil over high heat, then reduce the heat to medium-low; cover and simmer until peas are tender, 40 to 60 minutes.
Drain.
Heat soy margarine in a skillet over medium heat.
Add turnip and collard greens; cook for 2 minutes.
Stir black-eyed peas, garlic, and tomatoes into collard mixture; cook and stir until collards are tender, about 5 minutes.