"Off the mark" (and "on the mark") are idioms from archery. If your arrow doesn't hit the bull's-eye, it landed off the mark. "Off the mark," then, means inaccurate.
From my experience, it tends to be a polite euphemism. For example, suppose someone says,
There are no better widgets than the Whamdoodle widgets.
and I disagree. I could reply:
No! You're wrong about that.
However, that language is contentious and confrontational. Unless said good-naturedly among friends, it could be considered impolite.
Instead, I might say:
I think you're off the mark there.
One thing that makes off the mark a little more polite: just because someone is off the mark, doesn't mean they've completely missed the target.
So, on the Stack Exchange, off the mark would be a good idiom to use when you think that someone's response has merit, but you also think there is something amiss in the answer.
NOAD defines amiss as "not quite right." That would be similar to "off the mark."
Way off the mark, then, would mean "completely off target." That would be more appropriate when you want to point out a major error. In that context, way means: at considerable distance or extent; far.
To "kick off" means to start. It can be transitive or intransitive.
The phrase originates in sports, like other answers have said.
In contrast to what another answer says, the actions that are started can be either positive or negative.
For example, a big project at work could have a "kick off meeting" where the people working on it are introduced and the goals are discussed.
Best Answer
It's between these two definitions. If I say, "He's been off with me," or, "He's been very off with me," it means that things are not the same between us, that he hasn't been treating me like he normally does, that there's an awkwardness, issue, or something going on with him that's affecting his behavior towards me, like maybe he's upset with me about something I said or did, which I maybe don't even know what that something is because I didn't realize he took offense, got hurt feelings, or had whatever emotional reaction he had that's making things off between us as he maybe hasn't told me, or maybe he's just been in a funk or in a funny mood lately about something completely unrelated to me, but whatever it is up with him, the way he's been with me, the way our relationship has been lately, has been not like it usually is, and not in a good way. It's that strangeness in him and how it's affecting how he's treating me by his treatment of me being substandard that I'm commenting on.
Being that the usage is somewhat slangy or informal, I believe this definition from Urban Dictionary sums it up, as well: