For example, I’ve got 3 MUs used by some non-virus icebreakers, 1 MemStrips installed and I play the Deep Data Mining. What is the count of free MU to resolve this run ability? 1 or 4?
The memory from MemStrips counts towards Deep Data Mining. This is because Deep Data Mining doesn't actually use memory, it just looks at how much memory you have vs how much you are using. MemStrips gives you memory, with a restriction on what types of programs can use it.