Is it an Odd Word?

EXCEL, 79 bytes:

=MOD(SUMPRODUCT(LEN(A1)-LEN(SUBSTITUTE(LOWER(A1),{"a","e","i","o","u"},""))),2)

input:
This function can be placed anywhere EXCEPT A1
Put your word in question into A1.

Output: 0 if even, 1 if odd.

JavaScript (ES6), 34 41 33 32 bytes

Saved 1 bytes thanks to Arnauld:

s=>~s.split(/[aeiou]/i).length&1

• Odd word : returns 1
• Even words : returns 0

---

Previous solutions:

33 bytes thanks to Arnauld:

s=>s.split(/[aeiou]/i).length&1^1

• Odd word : returns 1
• Even words : returns 0

Another way without bitwise operators:

s=>++s.split(/[aeiou]/i).length%2

41 bytes:

(s,a=s.match(/[aeiou]/ig))=>a&&a.length%2

• Odd word : returns 1
• Even words with odd letters : returns 0
• Even words with no odd letters : returns null

42 bytes to return 0 instead of null:

(s,a=s.match(/[aeiou]/ig))=>a?a.length%2:0

34 bytes, breaks on words with no odd letters:

f=s=>s.match(/[aeiou]/ig).length%2

Saved 2 bytes thanks to Shaun H

s=>s.match(/[aeiou]/ig).length%2

Brain-Flak 206 196 192 178 + 3 = 181 bytes

Try it Online!

([]<{({}[((((((()()())){}){}){}){}){}()]){({}[({}())]){({}[({})]){({}[({}()())]){({}[({})]){({}<>)(<>)}}}}}{}{}}><>[[]]<>()()){(({}[<>(())<>()()])){{}({}())((<>)<>)}{}}{}<>({}<>)  

This requires the -c flag to run in ASCII mode adding an extra 3 bytes to the length of the program.

Ungolfed

([]<
{({}[(((((()()()){}){}){}){}){}()])
 {
  ({}[()()()()])
  {
   ({}[()()()()])
   {
    ({}[(()()()){}])
    {
     ({}[(()()()){}])
     {
      ({}<>)
      (<>)
     }
    }
   }
  }
 }
 {}
}
><>[[]]<>)
(<(()()<>)>)<>{({}[()])<>(({}()[({})])){{}(<({}({}))>)}{}<>}{}<>({}<{}><>)

Explanation

First store the stack height for future purposes

([]<...>

Then while the stack is not empty (assumes that none of the characters is zero)

{...}

Subtract ninety seven (and store 3 for later optimizations)

({}[((((((()()())){}){}){}){}){}()])

If it is not zero (i.e. not a)

{...}

Subtract 4 (and store 4 for later optimizations)

({}[({}())])

If it is not zero (i.e. not e)

{...}

Subtract 4 (and store 4 for later optimizations)

({}[({})])

If it is not zero (i.e. not i)

{...}

Subtract 6 (and store 6 for later optimizations)

({}[({}()())])

If it is not zero (i.e. not o)

{...}

Subtract 6 (store 6 because the program expects one later)

({}[({})])

If it is not zero (i.e. not u)

{...}

Move the remainder to the other stack and put a zero on the active stack to escape all of the ifs

({}<>)(<>)

Once all of the ifs have been escaped remove the zero and the six

{}{}

Once all the characters have been processed subtract the height of the offset from the originally stored height.

...<>[[]]<>)

Mod by two

{(({}[<>(())<>()()])){{}({}())((<>)<>)}{}}{}<>({}<>)