Reichu: What is this? Cicada-induced hallucinations? Can someone please tell me what the hell is going on?
The Eva Monkey: Film makers occasionally use a degree of surreal imagery or instances to convey something in a work of film. I believe this is essentially what we are seeing here. There is no logical reason why Shinji would be "hallucinating". Rather, I think that we are seeing his emotional state being conveyed by surreal imagery. Shinji is "feeling" his world closing in on and swarming about him, as if his present circumstances are tormenting him, regardless of the fact that he is running away from them.
Incisivis: The cicadas may represent the "sound" of his conscience, which he's covering his ears to block out, a futile gesture since the noise is coming from inside his head.
Gundampilotspaz: Perhaps the cicadas are just a manifestation of Shinji's internal turmoil. When he decides to run away, the cicadas suddenly stop. Like magic, no?
Reichu: In an earlier version of the script (published in Evangelion Original I), anyway, the cicadas are represented as being inarguably real and clearly have something to do with Shinji's reaction. In it, Shinji exits the theater and looks up, frightened, at the sky. He says to himself, "……I should go back… I should go to school……", abruptly followed by the first cicada. He then overhears an elderly couple out for a morning stroll stopping and listening to the cicadas. The "vision" is absent, but the end result is the same: Overwhelmed by the cacophony, Shinji covers his ears and runs away.
Referring back to a comment Shin-seiki made at 041, it would seem that Shinji started the morning planning to get his act together, but is, ahem, "deterred" by his environment.
Ark: Assuming the cicadas are real, maybe he finds cicadas to be an oppressive presence. I've been to Florida and they can get pretty loud.
Mr. Tines: Having lived for a while in warmer climes, I got accustomed to the way that when it got hot, the noise of the cicadas added an almost synaesthetic quality, where the heat "sang" or "seethed". It could get as loud as traffic, and shriller, and I can understand it getting to be oppressive in a "Shut up, I'm trying to think" sort of way. (These days, years later, when we do have a hot summer, I'm still disoriented by quite how quiet the heat is.)
OMF: Perhaps the cicadas are like the "character theme" for Tokyo-3, representing the underlying menace pervading the city. We never see them, but they are always about, chirping, endlessly chirping…
Reichu: When all is said and done, the cicadas remain a rather mysterious element to me. Are they real or not? Maybe it's a Hobbes sort of deal.