Forget 'clash' - that does have a different meaning. It can mean "to collide with a loud, harsh, usually metallic noise", but more often than not it is a deliberate collision. For example, the sound of cymbals is a 'clash', and the same word can describe them being played, ie "the cymbals clashed together". It doesn't usually describe an accidental collision.
A 'crash' is often the same thing as a 'collision' - for example, 'a car crash' or 'a car collision' are both idiomatic ways of referring to an accident involving one or more cars. The two words have distinct meanings though, and both carry different inferences. Sometimes, "collision" is used in a positive way. For example, when two people meet it is sometimes said that "their worlds collided". On the other hand, a car crash would almost certainly mean damage to the car and whatever it collided with - another car, or a tree, for example. If a car collided with a bird it is unlikely that the car would be damaged (although the bird might not fare so well). Bird strikes, as mentioned in your example, are notoriously dangerous for planes because a bird can get into the engine and cause damage to the plane, although your example text is saying that more often than not they are harmless. "Collision" definitely seems to be the best word here because of the varying outcomes that are possible.