Unfortunately, there aren't any readily available standard tests, as I don't believe they have established any guideline levels for blood yet. You can get home kits such as this one and get your levels, but it's really kind of an academic number.
The blood tests for porphyria (some people call it the "vampire" test) include an ALA level, but that's the only clinical one I'm aware of that tests for any of the Omega 3 fatty acids.
Also, be careful about suddenly just ingesting tons of Omega-3's, somewhere in the early 2000's the FDA published warnings of health risks associated with large quantity Omega-3 supplementation.
Part of the problem is that they just aren't really understood yet, so while they know that Omega-3s are beneficial and that the ratio is important, they haven't really established WHY they are important or what good levels are, that kind of thing.