So I was a sorcerer 1st, I wanna get to lvl 4, grab a feat, then multi class into cleric, specifically war for fluff reasons. Can I wear plate and still cast my sorcerer spells?
To be able to cast spells in armor, you must be proficient with that armor. Class does not come into it.
You must be proficient with the armor you are wearing to cast a spell. (PH p.201)
A first level war cleric is proficient with heavy armor.
There are other restrictions regarding armor, such as strength requirements, or that a druid will not wear medium or heavy armor made of metal. But these restrictions are not directly related to spell casting.