Signal path switching for effect circuits
If I am understanding the question correctly that is actually a fairly complicated matrix. So correct me if I am wrong.

What you are looking for is this...



If you really only want the four permutations you can do that with a four pole four way switch like this...







simulate this circuit &ndash; Schematic created using CircuitLab

However, the permutations are much greater than four, six using all of them and more if you skip one, two, or three effects. If you want all of them then there are many ways to do that, some with micros, but a simple enough solution can be implemented with 13 reed relays, a bunch of diodes, and a rotary switch.







simulate this circuit

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Note I only showed two switch positions, I am sure you can figure out the rest. I also added a bypass.