Is this an adverbial clause?

"How they are spoken" is a clause of manner or an interrogative clause, subordinate to the preposition "on".

"On how they are spoken" is then a prepositional phrase. As an alternative, you could say that "how they are spoken" is a noun clause that is the object of "depending on".

Now to "depending on how they are spoken". It is not a clause: it merely contains a clause. If you take "depending on" as a preposition, it is a prepositional phrase expressing a condition or something like that. Or could it be regarded as a participial phrase? Consider this sentence:

The age of your date? She may be old or young, depending on what you filled in as a preference on the site—don't you remember?

Suppose "depending" were a participle. Then it could be rephrased thus:

A. She may be old or young, while she depends on what you filled in...

This does not make much sense. A better rephrasing would be this:

B. She may be old or young, which depends on what you filled in...

It seems clear that "depending" is not a participle, or it would have belonged to the subject "she". Therefore it must be a preposition here.

Your example would give this, if it were taken as a participle:

A. Both can be quite strong, as they depend on how they are spoken.

Or it could be a preposition:

B. Both can be quite strong, which depends on how they are spoken.

The first interpretation is not entirely impossible, but I'd call it weak at best; the second one sounds much better. Therefore it is best considered a preposition here, which makes the whole phrase an adverbial adjunct of condition.

First let's define Adverbial Clause:

An adverbial clause is a clause that functions as an adverb. In other words, it contains subject (explicit or implied) and predicate, and it modifies a verb(wikipidia)

Hence in case it's an adverbial clause.