Hello! I see impact as something more direct, like when something hits a surface or another object, or when a situation caused another thing to happen. Physically, we can say that someone died from the impact when the car hit the wall. Also, now not physical, that the crisis impacted in prices increase. Influence is something more subtle, indirect. I can influence my friend to buy a mobile by saying that that model has more advanced features or the price is lower than others. In this case I'm just giving an idea, not determining whether he'll by it or not.

Yes, I use Urban Dictionary quite often but we cannot find where the word is used, if it's current used or not. For us non-native speakers sometimes it's pretty difficult to use slang or idioms for we're not sure if we would sound natural, sometimes we're took as old-fashioned or uneducated because we chose the wrong terms.