The original phrase can be extended/modified:
Лопоухий косой за песчаной косой пал под острой косой косой бабы с
косой.
The updated phrase uses the word "косой" with 5 different meanings. Extra words in the phrase help a non-native speaker to identify the meaning of each "косой" instance. Translation:
- лопоухий косой - lop-eared hare
- за песчаной косой - beyond a sandbank
- пал под острой косой - fell under a sharp scythe
- косой бабы - of a cross-eyed woman
- с косой - with a braid
Once that "explained" phrase is picked apart and understood by a student, then student would need to know at least two more meanings of the word:
- косой - skewed; crooked
- косой - cross-eyed man (as a noun)
Then a student can try to make sense of the original phrase:
Косил косой косой косой
There is a possibility of a double meaning here. The subject in this sentence could be a man, but in a context of a fairy-tale it could be a hare.
UPDATE:
Another aspect of the problem, in addition to the many meanings of word "косой", is the exact meaning of each word. Russian grammar is flexible and allows words to be moved around in a sentence. A teacher may list the following three (possibly more) word-order sequences:
- Verb / subject / adjective modifying object / object - Cut / cross-eyed man / with a crooked / scythe
- Verb / adjective modifying object / object / subject - Cut / with a crooked / scythe / cross-eyed man
- Verb / object / adjective modifying subject / subject - Cut / with scythe / cross-eyed / cross-eyed man
In the last example adjective and the subject restate the obvious (repeat themselves). That usage is unlikely in practice. The first two examples deliver the exact same idea in spite of individual "косой" words taking different meanings.