International Science Olympiads include Math (IMO), Physics (IPhO), Chemistry (IChO), Bio (IBO), Informatics (IOI), Astronomy (IOAA), and Linguistics (IOL).
Does receiving a medal at one of these events, or even medals from multiple events significantly change how colleges view your application?
More over, are these prestigious awards almost a guarantee acceptance for academic-heavy schools such as MIT, CalTech, and maybe even Princeton?
None guarantee you admissions at any school but they give you a HUGE push towards acceptance provided all other parts of your application are competitive too. Along with that, they are achievements that will be highly regarded all your life.
Nothing guarantees you admission anywhere unless your last name is Obama, Rockefeller, or Kennedy. Caltech loves international medalists though, but they are still very GPA and test score heavy. I know 2 people who got into MIT without International Olympiad medals (granted, one of them got one in chemistry a few days ago).
International Olympiad Medals are definitely helpful, but not a guarantee. Especially for certain schools who attract a lot, note they don’t want the ENTIRE group of ISO medalists. Some schools would have difficulty denying such student, but the top tier colleges have already a very strong enough student body and applicant pool to easily reject another Olympiad medalist. But what they do is demonstrate your interest and aptitude, which will help.