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Only eighteen words hold O second and E third, and most of them are plurals.
S takes eleven of the eighteen, a very high share. COEDS, DOERS, GOERS, HOERS, JOEYS, KOELS, NOELS, POEMS and POETS are all plurals of short nouns.
ZOEAE, ZOEAL and ZOEAS all come from zoea, the larval stage of a crab. Z opens three of the eighteen, which is remarkable for the rarest letter in English.
They are the only entries here a biologist would use and nobody else would. The rest of the page is ordinary vocabulary or archaic verb forms.
Both come from do, in the second and third person forms that English dropped centuries ago. They survive in the King James Bible and in Shakespeare.
POESY, an old word for poetry, belongs to the same register. Together they give the page an unusually literary feel for a group this small.
They differ in the fourth box only. POEMS tests the M and POETS the T, so neither rules out much of the other.
A cuckoo found across South Asia and Australia, named after its call. KOELS is the plural and the form that fits here.
A fine wind blown silt that forms very fertile soil. It is a standard term in geology and it doubles the S.
A warm dry wind coming down the lee side of a mountain. The word is German and the spelling has survived intact.