Grammar.yourdictionary.com provides examples of short vowel words as of 2015. In addition, Simple.wikipedia.org describes vowels in the English language. Wordfind.com also provides lists of vowel words, helpful for games such as Scrabble.
Vowels are the letters A, E, I, O, U, and short words with vowels have one or more of these letters. Examples of short words with vowels include "hi," "are" and "cog."
If one is not sure of the meaning of a short vowel word, it's possible to look up the meaning on dictionary websites. Dictionary.reference.com provides definitions for many words as well as pronunciation help. Vowels can also have different sounds or points of emphasis in words which effects pronunciation.