I currently live in an area of the United States with dense vegetation and hear thier songs every morning. Poetically you can refer to the sound that cicadas and crickets make as songs. "The cicadas and crickets are singing." Normally, "crickets chirp" and "cicadas buzz." You can also say, "the cicadas are shrilling." Once I was walking with a friend in the woods and he said, "the cicadas are crying." If you are looking for colorful ways of describing animals, poetry would be a good source.

you would say a cicada cries and that cricket cricks and if you wanted to know frogs croak. You sure have a lot of questions about animals.

The buzzing and clicking of cicadas.

The sound a cicada or cricket makes is usually referred to as a chirp. The sound that thousands of cicadas make together sounds like a four-engine airplane landing and has no word for it. I've heard it once and it's creepy.