∗ I'll be at my uncle's house you should need to reach me
is ungrammatical. You need an if in there: if you should need to reach me. The if is only omitted if should is inverted with the subject. The inverted construction is a ‘fossil’ from much older usage; today it is fading into disuse, and has a very quaint ring in the US. Once any verb might be used in this construction, but today only should, had and were are used this way.
The rest of your sentences are all ‘relevance’ conditionals: that is, the protasis (‘condition clause’, ‘if clause’) does not express a condition under which the apodosis (‘consequence clause’, ‘then clause’) is true but a condition under which the information in the apodosis is relevant. For the most part they all express the same thing, which may also be expressed with an ordinary if clause:
I’ll be at my uncle’s house if you (should) need to reach me.
However, there is another dimension to the versions with (just) in case. In case may express, alternatively or additionally, the reason why you will be at your uncle’s house: you will be remaining at a particular place (rather than going out) so that you can be reached if that becomes necessary. That is the primary meaning of the expression, as in
I’ll take an umbrella in case it rains.