"Hence" is not especially formal. It means either "consequently" or "in the future"."Ergo" also means "consequently" or "therefore", but it is Latin rather than native English and is indeed more formal, and actually old=fashioned. It might have appeared in mathematical or logical arguments, but even in academic contexts, a word such as "therefore" or "hence" would probably be preferred these days.

Hola Lupita, Although I have heard both used in conversation, I do not consider 'hence' and 'ergo' to be colloquial. Colloquial synonyms include 'therefore' and 'so', which is a bit more informal than 'therefore'. For examples of these words in different contexts, you should check out grammarist.com Espero que esta explicación le ayuda :) Marisol