Strokes typically are in arteries, DVT's are veins. Different plumbing. One's taking blood where it needs to go, the veins bring it back.
No, DVTs do not cause strokes, but can cause pulmonary embolisms if they break off. Your venous blood (which, by definition, is where DVTs are) travels to your heart, to your lungs to pick up oxygen, back to your heart, and finally to the rest of your body, including your brain, to deliver the oxygen. DVTs cannot physically get past your lungs, so they're unable to reach your brain.
I'm reading about PEs in my EMT book right now
I feel bad for you son
The answer, yes...if you also have a cardiac defect where there is a hole in the heart (PFO - patent foramen ovale) allowing blood to shunt from the right atrium to the left. That sort of thing is referred to as a "paradoxical embolus." It's pretty rare, but otherwise, no. PE would be the worst you could expect, but that's pretty bad.