A basic but limited solution is to use Conditional Formatting to
dictate what format to use depending on the value selected from the
pull down list. You are only limited to three Conditional Format
conditions however. But if you initially make the cell the format of
one of the four formats you wish to use, you can then use the three
Conditional Formatting slots to give you the remaining three formats
you require.

If you require 4 format possibilities for the same cell, this solution
may not completely answer your question. I can only think that perhaps
there is a VBA script solution that can achieve the same thing.