The meanings of 落ちる・墜ちる・堕ちる are slightly different.
There is a group of words in Japanese which, as with your examples, are pronounced the same but may be written using different kanji characters. The word おちる existed before these kanji were assigned to it. So what reason could someone have had to assign different kanji characters to おちる? The reason is that there were slightly different meanings to おちる depending on the context in which it was used. Assigning multiple kanji to the word was a way to account for the semantic variations of the word according to the context. The base meaning of the different kanji characters is the key to understanding the subtle difference between the words.
Accordingly:
落ちる denotes the simple concept of a falling movement from high to low. This can be a physical object falling, or an abstract thing like a mood changing from high spirits to a low feeling .
墜ちる describes falling as related to some kind of accident or trouble. It is not a mere movement from high to low, but rather has a nuance of something falling or collapsing under unfortunate circumstances.
堕ちる has a sense that along with a fall there is a loss of something. For example this kanji is used to describe things like fallen angels, demotions, scandals, etc. It has a subtle inclusion of some type of moral failure, or a loss of face of some kind.
It is certainly an interesting area of Japanese. I recommend checking out some other words which have the same characteristic. For example, よろこぶ, おさめる, はかる, etc.
I would also add that it is more common to see this phenomenon in manga and literature because they tend to prefer a more stylized use of words. Manga in particular is famous for its interesting manipulation of orthographic norms. So while this is an interesting question, it isn't something that you will come across all that often, in my opinion.
