Insights about the “mothmen” from clues in the film (SPOILERS)
The ‘mothmen’ are evil spirits or fallen angels (they're synonymous). This is clear when viewing eye-witness drawings of the creatures, which never show beautiful angel-like beings, but rather dark disturbing, obviously-malevolent winged-creatures. It’s the same thing with the actual appearances of the creature, like during the car crash (freeze frame the images).
A mothman CAUSED the auto accident that injured Mary Klein (Debra Messing). Would a GOOD angelic being cause such a tragedy (regardless of the fact that she ultimately dies of a pre-existing problem)?
The bible calls Satan the "prince of the power of the air"; hence, his filthy underlings (demons) are spiritual and electro-magnetic in nature. They can thus speak through a phone that's not plugged in or perhaps manipulate a traffic light. They can mimic the voices of dead loved ones or even take human form, like Indrid Cold, Mary or the male nurse who insists that Mary's drawings are of "angels" and then mysteriously vanishes.
The researcher from Chicago reveals that the mothmen are from “hell” (the spiritual underworld that underpins the earth) and send out mixed messages to ruin people’s lives. They may seem to be benevolently warning humans but, at the same time, are obvious instigators of human suffering (the car crash, Gordon's job loss, insanity & ultimate demise and the researcher's loss of his family, career & respectable social life). Also, they refuse to reveal their true selves and intentions. They are highly skilled masqueraders.
The reclusive researcher also points out that they have been around for millennia and therefore see things 2-3 moves ahead of humans; they use this vantage point to manipulate, deceive and destroy. Since their M.O. is to “kill, steal and destroy,” they feed on death, destruction and torment and therefore are attracted to the places where great tragedies will transpire, like the Silver Bridge collapse.
The saved police woman at the end was number "37,” historically a numerical symbol of The Christ, which shows that her submersion in the river and figurative resurrection is a type of the Messiah. Yet she is still a victim in that her previous views that the mothmen are destructive and manipulative could now flip-flop into the deception that they are somehow agents of good. Of course we never find out if this happens because the tale potently ends with Klein and Connie in shock sitting in an ambulance just glad to be alive.
The film powerfully illustrates that humanity is caught in a cosmic war and that there are malevolent beings who purpose to use, ruin and destroy people through deception and manipulation.
Of course this is a commentary on the data supplied in the movie and therefore doesn't necessarily have anything to do with the real-life story.