sound a lot alike, they are not synonymous (having the same meaning). Anomalous
describes something that doesn't fit a norm — an unfamiliar form of life or behavior, for example. Anonymous
refers to an unknown name or identifying characteristic.
From Edgar Allen Poe's Fall of the House of Usher:
To an anomalous species of terror I found him a bounden slave.
From Moby-Dick, by Herman Melville:
Physiognomically regarded, the Sperm Whale is an anomalous creature. He has no proper nose. And since the nose is the central and most conspicuous of the features; and since it perhaps most modifies and finally controls their combined expression; hence it would seem that its entire absence, as an external appendage, must very largely affect the countenance of the whale.
And, from Thomas Hardy's Return of the Native:
A person on a heath in raiment of modern cut and colours has more or less an anomalous look. We seem to want the oldest and simplest human clothing where the clothing of the earth is so primitive.