Elliot holds Blood higher than anyone else, almost to the point where Blood can do no wrong in his sight. Blood likes Elliot and won't insult him (much), but sometimes Elliot's short-sightedness and hero-worship unsettle and/or disturb him.
Tweedle Dee & Tweedle Dum
Elliot is annoyed by their constant slacking. Not to mention the fact that they're always insulting him (namely by calling a rabbit), pulling pranks on him, and constantly harrassing him. As a result, they tend to get in a lot of gun fights and argue nearly all of the time.
Because Gowland is Blood's enemy, Elliot does not like Gowland in the slightest. If he ever sees Gowland, he will try to shoot him or will glare at him. Gowland, however, bears no grudge against Elliot in particular and even calls him "a good guy."
Though he is annoyed that Pierce calls him a rabbit and nicknamed him, "Elli-Chan", he tolerates him and thinks of him as an "Ok guy". Elliot is one of the nicer Role-Holders when it comes to how they treat Pierce.
In part because she's the head of a rival territory and in part because of her violent habits, Elliot dislikes and distrusts Vivaldi. He'll insult her to her face and does not like when Vivaldi shows Alice attention. In return Vivaldi seems more amused than anything, at least for the most part.
Because Peter insists that Elliot is a rabbit and calls him a fool for not accepting it, Elliot grows easily enraged when interacting with Peter. Peter is thoroughly disgusted with him, while Elliot would love to kill him to silence him.
As Elliot does not know that Ace is Julius' subordinate who threw him into Joker's prison, he has no grudge against the Knight. He does, however, find Ace annoying when he constantly gets lost and asks Elliot for assistance. Elliot also does not know that Ace is supposed to kill him as part of his job for Joker.
Elliot hates Julius, bearing a grudge against him due to being imprisoned by Julius' subordinates in the past.
Nightmare and Elliot get along quite well overall. They go out for drinks together on occassion, and as long as the topic of their boss/subordinate is avoided, they remain in a great mood together. However, once Blood and Gray are brought up, Elliot insists he respects Blood more than Gray respects Nightmare, Nightmare insists on the reverse, and they can end up fighting.
Elliot and Gray are on good terms, as both are near workaholics and know what it is like to have to deal with a selfish boss. However, Elliot's constant attempts to compete verbally with Gray about who respects their boss more wear Gray out and frustrate him.
As Joker was the one to keep Elliot imprisoned, Elliot hates him. Joker does not like him in return, and Black Joker in particular is verbal in his abuse of Elliot.
The two do not get along for much the same reason Elliot and Peter do not get along: while both take pride in their work, Elliot refuses to admit he is a rabbit and this irritates Sidney to no end. As they are from feuding territories, this only makes things worse. However, in casual situations, Elliot does not appear to think as badly of Sidney as Sidney does of him, provided the Black Rabbit does not mention that Elliot is a rabbit.
While Jericho doesn't seem to have any particular hatred for Elliot other than their mafia rivalry, Elliot hates him because Blood does not like him. The hot-blooded March Hare is open about his dislike and will attempt to shoot him the moment he has a chance.