Speed of Light: Does Relative Motion Affect It?

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does the fact we are moving at 250km per second around our galaxy and 300km per second around other larger galaxys? have any effect on the speed of light? sure they arent that great compared to the speed of light but does it?
 
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No effect whatsoever. The speed of light is a constant in all reference frames. Even if you are moving at 99.9999...% the speed of light, the speed of light is still c.
 
The basic assumption of special relativity is that there is no such thing as absolute velocity, only one thing relative to another. So if you are moving 250 km/sec around our galaxy, the galaxy is moving 250 km/sec around us, and the speed of light (in vacuo) is c no matter who is measuring.