As a fellow learner, I will share my thoughts.
I recently heard of a method for learning the onyomi readings that involved dedicating movies to each sound group, and scenes in the movie to each kanji in the group. It teaches your brain to identify kanji with a period of time (the day in which you studied the sound group), and an element (in this case, a movie). Hence making it easier to associate the correct onyomi. I find it easier than going through the Kanji in conventional order, learning random readings one after the other. Another positive is that sound groups often share similar radicals/primitives.
For example, オウ:
黄,横,央,応,王,往,欧,殴,翁,皇,押,桜,奥,凹
You'll also notice that if the Kanji have a 2nd onyomi reading, it's usually quite similar to the first reading.
I've also found that another effective way to learn the Kanji readings is to learn many words. Memorize the shape of the word/compound, and the word reading. Eventually, you'll automatically begin to associate the correct reading with the Kanji. Currently I have been working through a word frequency list, learning about 50 words a day. I'll look up the word, search the meaning, read plenty of example sentences and move on to the next. After learning some 500 words in the last 10 days, I have managed to maintain a 98.5% correct percentage after some 1500 reviews in Anki. That's without explicitly learning how to write, or read any of the Kanji. Simultaneously, I learn about 20 Kanji a day, as described above. You'll find that many of the readings (and meanings) come naturally after you've seen them used in so many compounds.
People will often tell you that cramming words/kanji is a bad thing. However, I think it's necessary until you're at the point where you can read 80% of the text in question (which, correct me if I am wrong, usually equates to +-3000 words), hence giving you a platform to effectively learn vocabulary more naturally through reading exposure and context.