Hello,
My mom told me that putting in some oil, right after putting the bag contents in the water, before boiling the water, would flavor the soup. Well, I don’t taste any difference with or without oil. Am I only one to see that?
If It wasn’t clear enough what readymade soup is, just Google “maggi” or “knorr” 
Moving to Cafe Society for you (where the food-related threads go).
Depends on the oil.
Olive oil definitely has a detectable flavor. IME, butter noticeably improves just about everything.
I’ve never heard of that trick, but if you’re looking for a possible mechanism for it maybe the oil is supposed to help extract some non-polar flavor compounds from the spices in the mix, resulting in more flavorful soup?
If so, I would do it in the beginning, before water is added, otherwise I don’t see how the oil has a chance to mix with the spices and extract those compounds. Dissolving certain spices in oil before adding watery ingredients is a fairly well known cooking technique.