Quote from Atomic Science Manual:Edit
"Strange Matter is...well..strange. The methods of obtaining strange matter remain a mystery, but it is sometimes found near antimatter colliders..."
See pics for an overview.
This gives a 2% chance to drop strange matter. This costs massive amounts of power and has low success rates.
Strange Matter can be used to create Red Matter Explosives, which when combined with a missile module makes a Red Matter Missile. See recipe on pic below
If you have the resources and of course the available power, you can place the generators next to each other, thus saving the build cost. It will still take a long time to make Strange Matter but the more you have running the better chance of producing.