Aural refers to the ear or hearing, and oral to the mouth or speaking. Something verbal is expressed in words, either spoken or written. Listen to the aural sensations of songs from outer space when you've been gassed for your oral surgery. Then stay non-verbal because you can't use words for a long time after the dentist wakes you up.
Aural is related to the sense of hearing:
While the songs may be familiar, the delivery is the aural version of having one's stocking stuffed. (technorati.com)
Audio teams capture far-flung aural impressions to set the proper movie mood (Dallas Morning News)
Our second word, oral, refers to something spoken (rather than written) or something related to the mouth:
The Long Island Storytelling Network will be telling tales at the library on Wednesday to help revive the oral tradition. (Storynet.org)
Oral cancer has always been a bigger threat to men than women. (Washington Post)
Now what about oral vs. verbal? They both relate to something expressed through words, but oral is spoken and verbal can be spoken or written. Oral and verbal are often used interchangeably — both describe spoken words after all. But they're not always interchangeable. If your little sister sticks everything in her mouth, she has an oral fixation. If she can recite the Constitution by age two, she's quite verbal. Consider these quotes from articles about college basketball:
K-State basketball gets oral commitment from 7-footer Diaz. (Wichita Eagle)
Gipson is Kansas State's second verbal commitment. (Fox Sports)
Using those definitions, Diaz told K-State he'd join the team. He didn't sign any paperwork. But Gipson could have signed on the dotted line, or he might have just spoken his commitment.
Remember: if it's related to the ear or hearing, you want aural. If it's related to something spoken or to the mouth, it's oral. And although verbal can mean spoken or written, oral can only mean spoken.