single "a" and double "aa"
Long "aai", "aau" vs. Short "ai", "au"
The difference between the long and short versions of these sounds is simply the length that the sound is held for.
"eui" vs. "oi"
These two sounds are very close and difficult to distinguish. Both are diphthongs.
The "i" symbol is used for two different sounds. Except when following by a final "k" consonant, the "i" symbol stands for the long "ee" sound as in the word "meet". Phonetically it would be described as a high front tense un-rounded vowel. When it is followed by a final "k" consonant (the ik final sound), it is pronounced as a short "i" as in the English word "sit". Phonetically it would be described as a high front lax un-rounded vowel. Additionally, when followed by a final "ng" consonant the "i" phoneme is changed to an "e" allophone by some speakers.
The "u" vowel is also used for two different sounds. Generally, "u" stands for a sound similar to the vowel in the word "spoon". Phonetically it would be described as a high back tense rounded vowel. When followed by a final "k" or "ng" consonant (the uk and ung finals, respectively), the "u" symbol represents long "o" vowel similar to the one in the English word "oak". Phonetically it would be described as a nasalized mid back tense rounded vowel.