The most common and most likely answer to this crossword clue is the 4 letter word APES
A
P
E
S
More clues leading to the result APES
- Our cousins a nuisance, almost
- Animals exercise, when going outside
- Timeless recordings of animals
- Mimics monkeys
- Copies records, having missed start
- Copies topless pranks
- Takes off, dismissing odd characters from, say, press
- Animals appearing in tapestry
- Animals from those parts to the west
- Zoo animals? Some escape sometimes
Buddy explains!

The straight part
We know that "Oafs" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case oafs = apes.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does APES mean?
APES noun- A primate of the clade Hominoidea, generally larger than monkeys and distinguished from them by having no tail.
- Any such primate other than a human.
- An uncivilised person.
- One who apes; a foolish imitator.
- To behave like an ape.
- To imitate or mimic, particularly to imitate poorly.