死体 したい is the most general word to express "a dead body". 死体 has a nuance that you are seeing it as an object. 死人 しにん =死者 ししゃ: is "a/ the dead" The day of the dead 死者の日 Book of the dead 死者の書 死人 is a word that you recognize it as a person though they're dead already. 死んだ人 遺体 いたい This word is especially used by news reporters, police officers, and staff of the (criminal) Identification Section. It is a way of calling dead bodies with a feeling of respect. The Kanji 遺 of 遺体 means "to bequeath",遺す のこす(the same way of reading with 残す which also means "to leave something) "to leave something to this world when someone passes away to the other world". It's "a body that's left in this world." One's (last) will: 遺言 ゆいごん One's property/ inheritance 遺産 いさん 亡骸 なきがら This one is thought a literary word for a dead body. Particularly indicates "an empty body that the spirit has gone away from it". So this word emphasizing that it's empty, and it is a sad thing that people know them are knowing it's empty as the owner of the body(spirit) has gone forever. So it's a kind of emotional expression as iyuuki explained. 骸 especially means a skeleton 骸骨 がいこつ or a skull 頭蓋骨 as an outer shell to contain the inside including their mind/spirit. 亡骸を葬る なきがらを ほうむる 亡骸を埋葬する なきがらを まいそうする This word is used for the perspective of the family/relatives, lovers, or friends who mourn for the person's death. 躯 means a body especially the trunk of the body. A literary word that corresponds to 体, it doesn't always mean dead body. A physique 体躯 たいく This one almost never used in colloquial/daily conversation. Only in novels or other fictional works as it's known as a literary expression.

死体 means a dead body, 死人 means a dead person 遺体 means a dead body, which is a specific and formal expression for 死体. 亡骸 means an emotional expression for 死体. For example, he meet 亡骸 of his parent in the room and fell down. 躯(むくろ) is the ancient expression for 死体, so a lot of Japanese may not know its meaning. For me, I know 躯 because it is my favourite cartoon's character.

I am a native speaker of Japanese, though this is just my personal opinion.／”死体” is the most common Japanese word for "dead body", while "遺体" is another common one which is a bit formal. "死人" means "dead man" rather than "dead body". "亡骸" is a kind of literary expression that you often see in novels or poems. "躰" just means "body", which does not necessarily mean "dead" one.