I know nouns and verbs can have declension and conjugation, but is there something similar for adjectives and adverbs, in varying languages?

In languages where adjectives are inflected for case, number or gender, they are indeed considered to be declined. Note that the distinction between nouns and adjectives is not particularly old: it’s 18th century.

In the traditional grammar I know, adverbs are considered indeclinable by definition. They don’t have number, case, or person. So they are not considered to have declension.

In reality, adverbs certainly have morphemes indicating degree, and in many languages they can have case or number morphemes. (In ancient Greek, those are locatives: they are syntactically adverbs, but historically they are nouns with unproductive affixes.) But there has been no tradition in the West of running through all the morphological variants of an adverb, the way they do for nouns.