C172 Pilot reported another aircraft cut them and another aircraft off while in the final approach phase.

Narrative

I was approaching ZZZ from the SW in Aircraft X. With no traffic in the vicinity; I reported 10 mi SW and intentions to land straight in Runway XX. After that report Baron Aircraft Y reported a 3 mile final on RNAV XX. It was clear VFR at the time and it was clear that the Baron believed he had priority over the VFR traffic; which is clearly in difference to the FAR/AIM. I reported position and intentions again at 5 mi SW and believed the much faster Baron should have landed. I joined and reported a 3 mi final at which time the Baron also reported final (again) and asking my position; which I repeated. I located the Baron 1-2 miles behind me and advised him that I was ahead of him on final and that I was continuing. The Baron became somewhat abusive on the radio and executed a go-around stating repeatedly that I cut him off. The Baron operated erratically in the go-around; executing a mid-field turn to crosswind at which time he cut off a C152 Aircraft Z; according to the C152 radio broadcast; which entered the pattern and was on downwind during my landing. The Baron taxied to my tie down in a little of a threatening manner at which time I left the field. There needs to be some focus on reminding IFR pilots that they do not have priority over traffic that is in airport traffic patterns during VFR conditions. This problem seems particularly acute at ZZZ where the foreign students being trained there often land straight-in when practicing the RNAV XX approach during heavy traffic times rather than breaking off and joining the VFR pattern. I have often had to adjust my pattern to accommodate them. The NAME Aviation School should be made aware of the issue and this might be a good refresher topic for FAAST.