We don't use 明了 a lot. 懂了 and 明白了 are basically same things, but we use 懂 the most in conversation because it sounds the most casual. 明白了 has been used more when a subordinate talking to his boss. BTW you can use 知道了 as well.

Actually there is nuances among 明白, 明了and 懂, they are interchangeable for most of time. 1. 我明白/懂（你的苦衷）, meaning feel sympathetic about someone's story. 2.我明了/懂了/明白了，usually used when you suddenly have it all figured out. 3.我清楚/知道整件事发生的经过. meaning I am clear about/know the whole thing.

These words mean the same thing. Are they all asking you whether something or something has been understood? If we are discussing a question, do you understand? These words can be answered. But if someone much older than you asks you, do you understand the question? The best answer is to understand and show respect. I hope it will help you.

明白, 清楚, 懂 are interchangable in most of the contexts and they mean "understand". e.g. 我明白/清楚/懂了。 明了(keep in mind it pronounces Ming Liao) seems to only be used in modern poems or some kinds of writing. In everyday conversations it rarely appears.