The Straw Hats Pirates, excluding the Straw Hat Grand Fleet, are one of the pirate crews with the fewest members in the world of One Piece. Naturally, each member had to get Luffy's approval prior to calling themselves a Straw Hat, and the eccentric captain's standards are quite hard to predict. The rubber man even declined the Grand Fleet's proposal of serving under him. However, there is one surefire way to receive an invitation from Luffy; be a weird creature.
Luffy seems to lose any capability to think after encountering a creature beyond his comprehension, and his typical response is to invite said creature to join his crew. Brook was a first-hand witness to this. The Straw Hats first met Brook at Florian Triangle, where the skeleton man was sailing alone. Luffy immediately asked him to join his crew after realizing that he was a talking skeleton, and this was before Luffy even knew of his background or musical talents. However, Brook isn't the only one who received such treatment.
Unigaro and McTreenald
Like most places in One Piece, Thriller Bark had a diverse and interesting population. All kinds of undead were walking on the island, though they don't fit the classic definition of zombies. These zombies were the culmination of Dr. Hogback's medical expertise and Gecko Moria's Devil Fruit power. They created Frankensteined beings that are capable of thought and weird behaviors. Unigaro and McTreenald were two of the resulting creatures.
When Luffy got to Moria's ship, he encountered Cerberus, a three-headed zombie dog. He tried taming it but ended up being bitten by all of its three heads. He eventually lost his cool and punched the dog, forcefully making Cerberus submit to him. Luffy rode his newly-tamed mount and entered the gates, where he immediately found Unigaro and McTreeland. The unicorn zombie and the old tree zombie were caught having a drink. Baffled by their appearance, Luffy immediately sent them invitations to join his crew. Of course, Zoro and Sanji were quick to shoot down his proposal.
Hyoutauros
Similar to Thriller Bark, Punk Hazard was also home to unique beings. A portion of its population consisted of centaurs. These creatures were once human and were only turned into their current state using Law's Devil Fruits powers. Hyoutauros was a particular centaur Luffy took a liking to. He wasn't the brightest, proven by the fact he initially thought Luffy was also a centaur, and Luffy also knocked him down. But he eventually regained consciousness and chased after the Straw Hats, an act Luffy completely misunderstood. Luffy regarded it as a friendly action and tried to make him join his crew, to the annoyance of his friends.
Kin'emon's Legs
Kin'emon's introduction was one of a kind. The Straw Hats were greeted by a huge dragon just as they arrived at Punk Hazard. They easily dealt with it, especially since they just returned from their two-year training. Other than the fact that it's a live dragon, the pirates found it odd that a dragon could speak. They soon realized that the voice wasn't coming from the dragon per se, but from someone stuck to it. Only after they decapitated the flying behemoth and pulled the jutting lower extremity did they realize that it was nothing more than that -- a lower body.
It's Kin'emon's legs, to be precise, but Luffy and the rest of the gang weren't aware of his identity at the time. To make matters worse, Kin'emon's legs immediately attacked Luffy and ran. But that didn't stop Luffy from endearingly asking him to join his crew, which Usopp immediately interrupted.
Luffy has interesting tastes when it comes to choosing his nakama. If not for the other Straw Hats, his pirate crew might be able to double as a traveling circus.