For the chicken salad, beat cream cheese, mayonnaise, green onion, lemon juice and poppy seeds until blended. Add chicken and walnuts and season to taste. Chill until ready to assemble.
For pesto cheese, pulse basil, parsley, garlic and olive oil until a paste. Add cream cheese and pulse to combine, adding sour cream as necessary to make smooth. Season to taste and hold at room temperature until ready to assemble.
For the egg salad, grate eggs coarsely on a box grater. Toss with mayonnaise, olives and onion and season to taste. Chill until ready to assemble.
To assemble torte, line a 9-inch springform pan with plastic wrap so that it hangs over the sides. Remove crusts from sandwich bread. Cut each crustless slice of bread in half (so they are about the size of ladyfingers). Line the bottom of pan with bread slices, alternating whole wheat and white bread. Line alternating bread fingers up side of pan.
Spread chicken salad over bread-lined bottom of pan. Layer bread slices over chicken salad (alternating whole wheat and white again) and spread egg salad over. Repeat with bread slices and pesto cheese, and top with a final layer of bread slices. Pull hanging plastic wrap over top to cover and chill for at least 3 hours.
To garnish, top torte with remaining pesto (pipe as you would a cake). To serve, slice as you would a cake and serve with a side salad.