Really I'm trying to find out which objects make it impossible to complete the others. I'm assuming completing one Strand String makes it so you cant complete the others, or that completeing the UE string means you cant complete the Vonian one etc...

That's correct. You can complete the Miranu Nebulae Exploration string on any pilot file. You can only do one Ue/Voinian, and one strand mission string.

Though the Voinian isn't actually one of the "Central Objectives". There's also another topic right here on the first page with lots more info.

There are bugs (well, loopholes) allowing a second Strand string to be done if you start with the Igadzra string, and the Voinian and UE strings can be done simultaneously. My favorite string is the one that makes you a Captain of Freeport.