Superficially, your problem is the use of scanf - it stops at the first space it encounters. Using fgets is usually the answer - and that might have been that. There was another problem in that you did not terminate your string (which led to the interesting last character - quite by chance, I must add), and you did not check for overflow in either the input or output buffers. Most of these points were made in other answers.
However - the problem is quite a bit more interesting, and harder, because you are using "non ascii" characters in your input. I am guessing your robbers have Scandinavian roots. This means that you not only need to worry about whitespace - you need to be using "wide characters".
I took the liberty of rewriting your example in "wide" form - meaning that it uses 
fgetws   - the wide equivalent of fgets
wprintf  - the wide equivalent of printf
wcschr   - the wide equivalent of strchr
As well as "wide" strings like L"wide string", "wide" characters like L'å', and "wide" format specifier %ls.
A stylistic problem with your code is that really long if statement that consisted of a long series of OR-ed comparisons with individual characters. You can do one of three things:
- format more clearly with carriage returns and line continuations:
 
if( inputText[ipTextNum] == L'a' || \
    inputText[ipTextNum] == L'e' || \
    inputText[ipTextNum] == L'i' || \
    inputText[ipTextNum] == L'o' || \
    inputText[ipTextNum] == L'u' || \
    inputText[ipTextNum] == L'y' || \
    inputText[ipTextNum] == L'å' || \
    inputText[ipTextNum] == L'ä' || \
    inputText[ipTextNum] == L'ö')
Note: you did not test for space, so space is turned into o which is not what you want according to your description.
 2. Replace the whole thing with wcschr which looks for a character in a string; by searching for the character in the string of vowels (this is what I did in the code below - including test for space); or
  3. You could also create a function for yourself like
int isVowel(wchar_t c) {
  return wcschr("aeiouyåäö ", c)!=0;
}
To make it even more compact/readable.
Anyway - here is the complete, annotated code:
#include <stdio.h>  // <<<< dont forget your header files
#include <wchar.h>  // <<<< to be able to use 'wide' characters: ö etc
// define the max size of input and output string:
#define IP_MAX 100
#define OP_MAX 300
int main(void) { // <<<<< use the correct function signature
    wchar_t inputText[IP_MAX], outputText[OP_MAX];
    int inputLength, ipTextNum, opTextNum=0; // <<< initialize opTextNum to zero!!
//    scanf("%s", &inputText);  // <<<< triple NO:
                                // 1) scanf stops at the first space
                                // 2) if the input is very long you overwrite your buffer
                                // 3) you are passing the POINTER to the pointer to char;
                                //    you should use inputText not &inputText
    fgetws(inputText, IP_MAX, stdin); // read at most IP_MAX characters into inputText including '\0'
    inputLength = wcslen(inputText);  // length of wide C string
    inputText[--inputLength]='\0';    // strip carriage return
    //    printf("The length of the string entered is %d\n", inputLength);
    wprintf(L"you entered \n'%ls'\n", inputText);
    for(ipTextNum = 0; ipTextNum < inputLength && opTextNum < OP_MAX-3; ipTextNum++) {
       if(wcschr(L"aeiouyåäö ", inputText[ipTextNum])) { // <<< include test for space too
            outputText[opTextNum] = inputText[ipTextNum];
            opTextNum++;
        }    
        else {
            outputText[opTextNum] = inputText[ipTextNum];
            outputText[opTextNum+1] = 'o';
            outputText[opTextNum+2] = inputText[ipTextNum];
            opTextNum += 3;
        }
    }
    outputText[opTextNum]=L'\0'; // nul terminate the string
    wprintf(L"The robber said:\n'%ls'\n\n", outputText);
    return 0;
}
Output:
hello world
you entered 
'hello world'
The robber said:
'hohelollolo wowororloldod'