I was just having a conversation with a friend and I said "see how far from the access point each device is, so that I can do some relocation and such forth".
She said that using such forth at that part of the sentence is incorrect. Why?
The idiomatic phrase is "and so forth" which is often also used as a part of the phrase "and so on and so forth". It is, IMO, an elided form of "(and so it goes on) and so it goes forth".
While "and such forth" appears to be reasonably commonly used (going by Google's results), this ngram suggests that it is at best a colloquialism or a dialectal peculiarity and at worst, a common error.
To answer the question in the title, I'd say that and such forth should never be used. The phrase and so forth should be preferred instead.
So and such are merely variants of the same morpheme (like a and an, or he and him)
Such appears modifying (and quantifying) Noun Phrases, while so appears elsewhere. There are a number of idioms and fixed phrases that use them.
In the context here, so forth is the idiom because forth is an adverb. Alternate idioms with such include such things and such stuff; I would normally consider such forth to be a nonce blend of those idioms.
Like many other questions here on EL&U, while answering this question too I find myself standing on the crossroads of context.
As far as I can understand from the dialogue between you and your friend, if you were trying to convey that the distance of the devices from the access point allows you to do relocation and similar activities, then
so that I can do some relocation and such.
would had sufficed.
But if you meant to say that the distance allows you to do relocation, as well as some other activities, then the statement as it is does not convey it.
I'm guessing you used it as some sort of portmanteau of such and so forth, but I'm only guessing.
That having to guess is enough to cast doubt on its correctness, or at least its usefulness.
I think it is also used to avoid repetition in contexts when it is clear the sort of similar things you are referring to but unable to mention them . For example, processed foods are unhealthy because they contain colourings, additives and so on and so forth