Put potatoes into a large pot, cover with salted water, and bring to a boil. Reduce heat to medium-low and simmer until tender, about 5 minutes. Drain and cool. Bring a pot of salted water to a boil, add carrots, and cook until tender, 3–4 minutes. Using a slotted spoon, transfer to a plate and cool. Add peas to pot of water and cook for 30 seconds; drain and cool.
Whisk together ¾ cup mayonnaise, sour cream, oil, lemon juice, half of the garlic, and salt to taste in a large bowl. Cover and refrigerate sour cream mixture until cold. In another bowl, whisk together remaining mayonnaise and garlic; gently fold in crabmeat. Cover and refrigerate crab mixture until cold.
Gently mix sour cream mixture with eggs and onions along with the reserved potatoes, carrots, and peas. Cover and refrigerate potato salad until cold.
Just before serving, mound potato salad onto a round serving platter and form into a large cake. Spread crab mixture evenly over the top and sides. Decorate top of salad with salmon caviar (arranging it in the shape of a crab, if you like) and dill sprigs. Arrange pepper strips around the base of the salad. Serve immediately.