I don't know that a radar would provide enough of a warning anyway, if it could even see a single bird. And all it takes is one. The majority of birdstrikes happen near the ground, and the things I've seen have tended to be more to keep birds away from airplanes rather than trying to dodge them. They use cannons/noise-makers at many airfields and other means to keep birds away from low aircraft. And I've heard that the spiral painting on the compressor cones of many big jet engines, in addition to giving a visual indication that the engine is running, has a side benefit that, to a bird, it looks like the eyes of a predator and tends to scare the birds away from the engines. There have been mixed studies on the efficacy of that claim, but I don't know that any scientific research has been done to give a real yes or no. Boeing will claim that it doesn't matter. JAL claims that they had fewer birdstrikes on aircraft with painted spinners. I don't really know if it works or not.
In my experience, you aren't going to see-and-avoid most birds. You're simply moving too fast for either of you to get out of the way. I quit flying with only a few thousand hours, and I've hit several birds. And I don't know very many pilots who haven't either hit one or had a near miss. I've even been hit by a goose in my door when I while I was teaching in a 152, one of the few times that I can actually say the bird hit me and not the other way around.
The best way to keep from hitting birds is to try to avoid areas where birds are known to be flying, especially during migratory seasons. If you hear reports of a flock of birds at your airport, use a lot of caution. And report them if you see them. Try to minimize low flying. In most small craft, it's unavoidable. Your normal operating altitude is fairly low and right within the area that birds tend to fly. In bigger aircraft, try not to dally at lower altitudes, if you can help it. Climb to your altitude And if you're low to the ground (landing or taking off) don't put the aircraft in danger by trying to dodge birds. And every takeoff should include an idea of what you're going to do if you do hit birds.
"About 41% of reported strikes with civil aircraft in USA occur while
the aircraft is on the ground during take-off or landing and about 75%
of strikes occur at less than 500 feet above ground level (AGL).
However, over 4,200 strikes involving civil aircraft at heights above
4,500 feet AGL were reported from 1990-2013 in the USA and over 430 of
these were at more than 10,500 feet. The world height record for a
bird strike is 37,000 feet (Griffon vulture off the coast of Africa)."