Elliot's entire motivation for killing certain members of his family were for Leo. This was due to Humpty Dumpty's influence over him; anyone that held malicious intents for Leo were beheaded. Elliot, unwittingly, prioritized Leo, whom he had known for 2 years, before his family. His complete protection over Leo is another demonstration of their relationship.
Elliot's last words were also addressed to Leo. ("I'm sorry, Leo.")
After Elliot's death, everything was in chaos, but none were affected as much as Leo. His "other half" was gone forever. Instead of trying to find closure, Leo decided to erase his existence because he believes, like Vincent, that Elliot can have a happier life without him. He is hurting himself beyond belief, loathing his existence and the contracting incident because of the bond the pair once shared.
Oz and Leo have a very thin relationship. In the anime episode "Elliot and Leo", Leo sticks up for Oz saying that it was indeed Elliot's fault for spoiling a book. After this event Oz and Leo have always tolerated each other, and often helped each other.
Oz had considered Leo to be his friend. Leo denies this after Elliot's death, saying that they only bonded due to Elliot. That could be intended, however, as a way to hide any doubts Leo had about his actions. Oz continues to try to help Leo, and they unite for a common purpose to destroy the Intention of the Abyss for the final chapters.
Vincent is the one who told Elliot's last words to Leo, as he is the last person Elliot spoke to before his death.
Leo had stated that he and Vincent had some similarities, as their existence made someone important to them suffer, and they wished for their existence to be erased.
Oswald and Leo has a rather harsh strict relationship.
Levi's reaction towards the whole world's destruction as a hilarious story irritates Leo through the core. However, Levi says he admires Leo's determination more than his cowardice and undecisiveness.