"Taste" in your example is a 'sense verb'. Verbs like this require an adjective such as "strange" as predicative complement (PC), but not an adverb. Thus the example you gave is ungrammatical because the corresponding adverb "strangely" can't satisfy the complement requirement of the verb "taste".
The PC is describing the apple, specifically its taste, not the manner in which you physically taste it; you could also say "This apple has a strange taste" with no change in meaning.
"Listen" is different: it's not a sense verb and hence it can take manner adverbs like "carefully", "attentively" etc., as modifier: they are describing the manner in which you listen.
It's useful to remember that obligatory elements are always complements: they are needed to complete the meaning of the verb phrase; adverbials are always optional elements. In your example, "taste" requires an obligatory element to complete its meaning (you can't just say *"This apple tastes") and hence that element must be a complement, in this case a PC, not an adverbial.
Note: There are, however, one or two verbs that do select a manner AdvP as complement, as in "He treated her appallingly" where the AdvP is obligatory. And AdvPs also occur as complement to the verb "be" in its specifying sense, as in "The only way to do it is very slowly".
"Taste" in your example is a 'sense verb'. Verbs like this require an adjective such as "strange" as predicative complement (PC), but not an adverb. Thus the example you gave is ungrammatical because the corresponding adverb "strangely" can't satisfy the complement requirement of the verb "taste".
The PC is describing the apple, specifically its taste, not the manner in which you physically taste it; you could also say "This apple has a strange taste" with no change in meaning.
"Listen" is different: it's not a sense verb and hence it can take manner adverbs like "carefully", "attentively" etc., as modifier: they are describing the manner in which you listen.
It's useful to remember that obligatory elements are always complements: they are needed to complete the meaning of the verb phrase; adverbials are always optional elements. In your example, "taste" requires an obligatory element to complete its meaning (you can't just say *"This apple tastes") and hence that element must be a complement, in this case a PC, not an adverbial.
Note: There are, however, one or two verbs that do select a manner AdvP as complement, as in "He treated her appallingly" where the AdvP is obligatory. And AdvPs also occur as complement to the verb "be" in its specifying sense, as in "The only way to do it is very slowly".
PaulM
Thank you Paul, I really appreciate your detailed answer.