How long would you keep this Caesar dressing

Up to 7 days (homemade mayo as well). Egg whites/yolks out of the egg (but not combined with the acid) can last 3-4 days refrigerated, and eggs in-shell are good for 2-4 weeks depending on processing.

I can't speak specifically to the shelf life of salami, especially considering all of the factors that come into play (source, type, age, storage, etc.), but when dealing with meat in general, you should never eat it if it smells or tastes "off". Smell is really the most reliable means of determining whether or not meat is still good - far more reliable than the use-by date.

It's unusual for meat to smell or taste sour as a result of foodborne bacteria; sourness is more likely to be due to rancidity of the fats, which is of course equally dangerous, albeit in a different way. Oxidation is very likely if the meat was not properly wrapped and/or stored in an airtight container.

Of course, many people have trouble telling the difference between spoilage due to rancidity and spoilage due to bacteria, and so what you're perceiving as rancid (sour) may really be bacterial spoilage.

Either way, if it tastes off, it's spoiled; don't eat it.