It seems almost as if there were types of adverbs similar to the way Klingon has types of verb suffixes. {vaj} could be adverbial Type 1, {chaq} adverbial Type 2, {tugh} Type 3, and {batlh} Type 4. You probably can’t have two of the same Type, and you can have zero or one of each type in any verb clause.
We could then look at other adverbials and argue over which one belongs to which type and have a good old grammatical battle over it.
I think that there's a natural ordering imposed by the meaning you want to express in a specific sentence, but I don't think the order is fixed in general, or that you can't have two of the same type. For example, it seems clear to me that {vaj} and {chaq} should typically come before anything else, but I'm not sure that you can't say either {pe'vIl tugh nuHIv} or {tugh pe'vIl nuHIv} depending on what you want to emphasise between {tugh} and {pe'vIl}.
I'm also not sure that {vaj} has to come before {chaq}. I think {vaj chaq...} "In that case, perhaps..." and {chaq vaj...} "Perhaps, in that case..." are both sensible constructions, depending on whether the consequence is conditional or not.
And even though one adverbial may typically or frequently precede another because it's the more common situation, I don't think the other order is ruled out when it's warranted.
{chaq tugh nuHIv} (I don't know when the enemy will attack us; perhaps it is soon)
{tugh chaq nuHIv} (I know the enemy will act soon; perhaps they will attack us)
The combination {chaq tugh...} is probably much more common, but I can see {tugh chaq...} making sense in some specific contexts, or for emphasis ("SOON the enemy may attack us").
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De'vID