Do I need to inform my PI about every single project I am working on? I feel like my PI doesn't care much about my thesis (as if I already had one), and keeps assigning me several unrelated tasks to support the publications of his postdocs. Even worse, I don't feel like he is my "academic" advisor: every weekly meeting revolves around grant writing and research expense rather than the experiment itself. And the worst? We differ in our approach to science: his is data-driven, mine is hypothesis-driven.

At the same time, I greatly enjoy the mentoring I have been receiving from three  members of my thesis committee. We did have many exciting sessions of exchanging ideas and fruitful follow-ups. I feel like with their help, I am becoming the kind of scientist I always try to be. Last but not least, although they are experts in different fields, they respect each other and are happy to collaborate through my thesis.

Here is my problem: I have several ideas with each of my three committee members, and want to turn them into publications. However, these are deemed not the interests of my PI's lab. Do I need to inform my PI that I am working on these projects? Do I need to describe these projects in detail (he will yawn his way through the meeting anyways)? And if I can get some publications, should I put my PI's name there?
In your comments you mentioned that you are funded by your PI, which changes the dynamics and expectations somewhat between you and your PI; and I think he needs to know how you are spending your time.

My suggestion would be to seek approval from him to work on these. This is to show him that you are respectful and value his opinions on if these are worth working on. It can be in the form of I have some ideas I would like to develop with Prof xxx and Prof yyy, can I go ahead and discuss with them? 

Your PI would probably also need assurances that working with them does not compromise too much in your abilitty to support his lab. And lastly remember this. It is in your best interests that relationships between your advisor and you remain cordial.