How do droids increase their soak value? Can they get armor?

Sure. They can either wear it like an organic being would or have it bolted on like a carapace, whichever fits the story and/or character concept.

Remember too that multiple sources of Soak will stack (Brawn score, talents, armor, cybernetics) but not the same source (you can't layer two sets of armor and add them up).

Yup, they can "wear" armour. Check out the "Droids and Equipment" sidebar on page 47 of Edge of the Empire . Droids can either use equipment normally, or it can be integrated into their bodies at the GM's discretion.

...and then you can have their plating upgraded. Just imagine 3PO's soak value for most of Episode 1, compared to after he gets his gold plating.

Thanks. I thought that was the case.