Two Letters

AA: (n.) Lava having a rough surface.
BCFKM (AA) HLS

AE: (adj.) One.
DFGHKNSTVWY (AE)

AI: (n.) A three-toed sloth.
JKRSTW (AI) ADLMNRST

EA: (n.) A river or watercourse.
KLPSTYZ (EA) NRSTU

EE: (n.) An eye.
BCDFGJLMNPRSTVWZ (EE) KLNW

IO: (n.) A variety of moth.
BG (IO) NS

OE: (n.) A small island.
DFGHJMRTVW (OE) S

OI: (interj.) Word used to get one's attention.
BHKMP (OI) KLS

OO: (n.) Archaic term for the Greek letter omega.
BCDFGHLMPRTWZ (OO) FHMNPRST

OU (n.) An extinct Hawaiian songbird.
FLMSY (OU) DKRST

Three Letters

AIA: (n.) In India, a female servant or maid.
R (AIA) S

AUA: (n.) A variety of edible fish in New Zealand.
P (AUA) S

AUE: (interj.) Variant spelling of OW.
No single-letter extensions to this word exist.

EAU: (n.) Water.
B (EAU) SX

Four or More Letters

EUOI: (interj.) Ancient Greek cry during Bacchic revels.
No single-letter extensions to this word exist.

AIAIA: (n.) A variety of roseate spoonbill.
No single-letter extensions to this word exist.

EUOUAE: (n.) A method of memorizing psalm tones for Gregorian chants.
No single-letter extensions to this word exist.

While the most important ones are the two letter ones and they're extensions, the rest are still useful to be aware of. Note that for these purposes, Y is not considered to be a vowel (since Babble will never give you Y when you purchase a vowel).

Words are listed by length, with definitions. Letters that can be attached to the beginning or end of each word will be below that.

The way extensions are written are that the letters on the left side of the word in the parenthesis can each be attached to the right of the word, and likewise for the letters on the left. This is not to say that the letters on the left and right can be attached at the same time. For example, IO can become BIO or ION but not BION.

The two-letter words are (in my opinion) practically required for their general utility, but even the longer words can sometimes be useful: