Hi,
I saw him stealing the money (past tense verb+ing) As already pointed out, this stresses that you saw him 'in the act'.
I saw he steal the money (correct) Incorrect. You need 'him', not 'he'. This stresses you saw the completed act.
I saw he stole the money (incorrect) - can someone explain to me why is this one wrong? It's not wrong. This states a simple fact about the past.
I saw he was stealing the money (correct) - This states a fact about the past. To native speakers, the use of the continuous instead of the simple past 'stole' suggests that perhaps the act of stealing was not completed.
Best wishes, Clive