Views exposed filter, filter on multiple fields with dropdown and one textbox
If I understand correctly: you want to expose 3 dropdown filters, but allow only 1 of them for input.

You can hide or show filters by using views dependent filters: https://drupal.org/project/views_dependent_filters, but then you need a filter that sets up 3 values for showing 1 of your 3 independent filters.

But, why don't you use OR instead of AND with those filters? It would give results and you can sort it as you want.