Summary
Typing
/msg? group message
will only send to online members of that group, unless they have that long-winded-option picked, then they'll get it anyway.

Detail
Since some groups' messages seem to be only relevant for a short period of time, you can now send a /msg to only people that are currently online. This is done by simply appending a question mark, ?, to the /msg command. For example, if I want to send a message to only the content editors that are active, I could do:

/msg? content_editors Only those of you on right now will get this message!
Note the ? after the /msg. This could be useful for questions only useful for a short while, such as "Does anybody besides me think SomeDumbTroll is just a troll, and not just a misguided newbie?".
But what if you're one of those paranoid people who likes a full Message Inbox? Then you can simply visit user settings and make sure the option with the verbose description that reads something like "get online-only messages while offline" is checked. You currently have this option disabled, so you will only get online-only messages while you are on E2.

Random Notes

Q (not FAQs, since there is only one question that has been only asked once)

Does online-only /msgs ignore cloaked users?
No, online-only sends to everybody online, regardless of their cloaked status. (Essentially, being cloaked only changes other users' displays, nothing else.)