Mikagura Detective Agency is a three episode OVA, at 30 minutes each. It was released in 2004. And is based on a game by ELF.
It was Taisho era. Mikagura Tokito is the director of a detective agency that is famous for all the cases it has solved. One day he disappeared after being involved in an accident. Tomoe, Shigeno, and Chizuru, who adored him, were anxious about him. Hearing that Shigeno’s elder brother had seen him at a church in a foreign country, they travelled there hoping to meet him again.
However, it was a dead body of a priest in a church that they found there instead. Furthermore, they found his arms had been cut off from his body. Because they thought his death had something to do with Tokito’s disappearance, they decided to investigate the case. Suddenly they were attacked by men. There’s obviously tons of danger here, but they are desperate to find Tokito.
Porn seems to be the only genre where fellatio can be used to greet someone. I didn’t find the DVD or the game for Mikagura Detective Agency/Mikagura Tanteidan, but I did find game guides. Go figure. Check on this streaming service.