General answer to you and everyone else who asks the question Can I say X? without providing any context for saying X: You can say anything you want to anyone you want at any time you want and anywhere you want. The important question is Are you prepared to accept the consequences of what you want to say? Unless you are, don't say it.
Specific answer: If the chair has arms, then you should probably say "Get out of that chair". For a chair without arms, however, "Get off the chair" is standard. "Get off the couch" is correct.
None of those sentences is polite English, though. They're like direct orders in the military from a superior officer to an inferior officer or enlisted person. They indicate annoyance, impatience, anger, or some other negative feeling. They sound haughty and imperious.
It would be polite and probably not cause a fight if you said "Please get off the couch" or, even more polite, "May I ask you to get off the couch?" In both cases, however, you'll probably need to give a reason. The person you're asking to get off the furniture is going to ask why he or she should get off.
You'll get better answers if you ask better questions. Specifically, if you provide some context for your question. This one has no context beyond a disembodied sentence. We have no idea who you are (i.e., your role in the scenario) or who the sitter is or why you're supposed to ask the sitter to get off the couch. Maybe you work in a furniture store and want to ask a tired or lazy or sleeping customer to find a coffee shop or a hotel instead of sitting or sleeping on your merchandise?
I think OP's specific context is a (very slightly) "abnormal" usage, where most native speakers would probably say "Just because" (i.e. - for no particular reason that I can articulate).
In other contexts, just like that is normally used to mean as quickly as that, or with no further deliberation. In such contexts, that references a short (or even, non-existent) antecedent discussion/preparation.
The British stand-up comic Tommy Cooper used "just like that" as a catch-phrase - usually as facetious wordplay (not like this, [just] like that!), after a bungled "sleight-of-hand" magic trick.
Best Answer
By and large get off is proper in two circumstances:
When the idiom for the activity which you’re ending involves being on something. We speak of being on the telephone or on the treadmill or going on line, so it makes sense to end these by getting off.
When the idiom for being uninvolved in the activity is expressed with off. We speak about being off work or off duty, of being off rhythm or off our feed, so it makes sense to enter those states by getting off.
But the idiom is not ordinarily extendable to other situations. And you have to be careful. As Wendi Kidd has discreetly pointed out, get off has an explicitly sexual meaning, to achieve orgasm; and although that meaning is frequently extended to non-sexual activities in the sense “experience a rush of excitement”, or even simply “enjoy” (I get off on answering ELL questions), it’s still not a meaning you intend. If you say “I just got off reading the novel” people will probably think you are making a different mistake than the one you’re actually making!