The first pair is: in case of vs in the case of; the second is: I used to vs I'm used to.
Let's look at the first one first.
In case of (without the) is followed by a noun or noun phrase like fire or by a verb phrase. Here are a few common examples:
In case of emergency, call 911
There's a fire extinguisher on the wall in case of sudden fire.
I carry a heavy sweater in the car in case I get stuck during cold weather.
We sometimes use the phrase just in case without a specific noun or verb phrase; the idea of an emergency or some other extraordinary or special situation is understood.
Why do you carry that flashlight all the time?
Just in case. [Just in case I need it.]
Here are some more examples:
Let's take the car just in case the busses aren't running.
If I were you, I'd bring her flowers, just in case she's still angry.
It's better to be careful, in case of a riot.
In other words:
In case of x = if/when x happens
We can substitute the event for case, but we cannot use the case, which is used only in the similar but very different structure that follows.
In the case of ... (or, sometimes, in a case of) means the same thing, and is used in the same situations, as the Polish phrase w przypadku czegoś. It is sometimes contrasted with this case or that case, for example, in the following:
In this case, the director sacked the employee. However, in the case of Henry Jones, the employee got only a reprimand and kept his job.
The formation In the case of, the words the and of can be replaced by using a possessive or other determiner:
In Bob's case, the deal fell through, but in Mike's case, they honoured the contract.
but we can also say
In the case of Bob ... in the case of Mike ...
Some more examples:
In the case of public demonstrations, the police are less likely to use force.
The policy you're citing is only true in a case of employee insubordination. This case is something else entirely.