The first three have slightly different usages.
"In doing so" is typically used to mean "as a result of". The first item directly causes the second item, but the second item might not be what was intended to happen.
"So that" also means "as a result of", but is usually used when the result is intended, instead of a coincidence. It implies the first item was done in order to bring about the second.
"in a way that" is similar to "In doing so".


I couldn't get what is the difference between these:

"in a way that" is similar to "In doing so".


In addition, would you tell me if these are interchageable? if not, when? or when they are? I think you use 1 and 2 always and interchangeably for two reasons== purpose and introduce a result.

1. so that
2. in order that

in this way= in a way

in doing so

in such a way that