Best Answer - Chosen by Voting
"Så" is the direct translation of "so" and it works in most cases. The other words does not mean "so" but it's possible that a Swedish sentence using any of the following might be translated to "so" because it would sound weird in English otherwise. Also remember that "so" has two meanings in English. One when giving a reason for doing something and the other when say something like "it was so nice".
Det = that, it.
Varför = Why, which is why.
Därmed = Thus
Så till den grad = To the degree/point...
Mycket = Much, very
Vid = By, with, at.
Det var så kallt att det frös till is omedelbart.
It was so cold that it froze to ice immediately
Det var väldigt kallt _varför_ vi gick in direkt.
It was very cold _which was why_ we went in immediately.
Both in English and Swedish you can say "så"/"so" instead of "varför"/"which is why"
Så/därmed var sagan slut!
Thus the story was over!
Det var väldigt varm, (så) till den grad att det inte gick att vara ute.
It was very hot, (so) to the point that we couldn't be outside.
"Så" and "so" can be dropped.
I can't think of a situation where "mycket" or "vid" could ever be "so".
