Sherlock:
The most amusing way to annoy Sherlock is to play a note wrong on the violin. You can both play s whenever you get annoyed at him you like to get yours out and play a song. You always play a song he knows and will purposefully play the wrong note or play a section out of tune. It is fun to watch his nose wrinkle up and see him wince at each incorrect note. He usually will end up either taking the instrument from you or playing the song after you have finished correctly. It is a way to annoy him without making him mad.
John:
The best way to annoy John is with the simplest things. Not putting your cup on a coaster is one. You will both on purpose and on accident sometimes not use a coaster. It is amusing to watch him scowl and grumble about it. Sherlock will do it as well and you both laugh about it together. One day you both filled at least a dozen and half cups full of water, tea, and coffee and left them around 221B for John to find.
Mycroft:
It is easy to irritate Mycroft. One of the simplest things that will drive him crazy is if you call him anything but Mycroft. His full name is Alexander Mycroft Chad Holmes and you loved to use any variation of that you annoy him. You called him Chad, Alex, Myke, Alexander, and of course Mykie. It was highly amusing watching his eye start to twitch as you called him anything but his preferred name.
Greg:
Greg is not a terribly neat person. His desk is usually in some sort of disarray but he always claims he can find everything. The best way to get under his skin is to organize it just a little. You never actually fully clean it but you will put certain things away so that he just gets annoyed. You mostly do it if you're upset with him over one thing or another. But sometimes it's just because it bothers you.
Moriarty:
Your favorite way to bother Jim is to hide things from him. Mostly his phone or his keys. It's fun to watch him rush around the house trying to find them and in the end just hold it out to him. Usually he will then chase you around the house till he finally catches you. Then you usually make him kiss you before finally giving them up and letting him leave. It bothers him when he can't find them but the chasing is always amusing.