Lately I’ve become confused about the correct usage of much when relating quantity.
For example:
I put too much of the new oil
or
I put too much new oil
I put too much of salt
or
I put too much salt
Is ‘of’ correct if there is no article following?
Are any of the above incorrect?
None of your sentences sound correct to me. I’d say correct versions would be:
I put in too much new oil
or
I added too much new oil
I put in too much salt
or
I added too much salt
I put too much of the new oil
Okay. Puts emphasis on the new oil, like “too much of THIS.”
I put too much new oil
Okay.
I put too much of salt
Never used.
I put too much salt
Okay.
Is ‘of’ correct if there is no article following?
Sometimes. Seems to need some kind of specific indicator, though. “Too much of his paint” sounds okay, “too much of green paint” doesn’t.
I agree that they need “in” to be proper sentences, but perhaps they were just meant to be sentence fragments: “I put too much new oil [in the engine]”.
Otherwise, I agree with Gary.
That was my assumption.
Sorry yes, those were sentence fragments not complete sentences.
This kind of thing is tricky
“Don’t use too much salt.” - you’re referring to salt in general
“Don’t use too much of the salt.” - you’re referring to a specific quantity of salt that the hearer understands you to be referencing.
“Don’t use too much of salt.” - unidiomatic
It wouldn’t be a proper grammar thread if someone didn’t point out that “none” takes the singular verb, now, would it? 
I agree with GaryT and ascenray, FWIW.
[Proofreads vigorously for evidence of Gaudere’s Law]