Should I learn kanji readings

Yeah this has already been answered in the first post but just to clarify: The Kunyomi is used when the kanji is by itself or the only one in the word (single kanji words). The Onyomi is used when multiple kanji are used to form one word (compound kanji words).
E.g. 木 - き - tree
木曜日 - もくようび - Thursday
This of course is a general rule as there are exceptions where compound kanji words have both onyomi and kunyomi readings for their kanji.
E.g. 仕草 - しぐさ - gesture
仕 - し (Onyomi)
草 - くさ (Kunyomi)

As for the learning of Kanji, the method which BigEm was referring to other than wanikani was the MIA (mass immersion approach) I believe. Theres an interesting thread on it here: MIA or WaniKani.
Basically it has you learn just one english word closely associated to each Kanji which acts as a placeholder meaning until you can intuit the kanji readings/meanings later by learning vocab or context which the Kanji is used in. You achieve this by consuming a lot of native content and essentially immersing yourself in the Japanese language.
This contrasts from WaniKani in that Wanikani has you learn readings as you go along with vocab to go with those readings. Wanikani you see results straight away and can immediately use the kanji/vocab youve learnt whereas MIA requires you to go through at least 1000 kanji before you even start to learn readings, and you learn readings by looking up words you encounter after this phase.