Translation:I want sushi.
My undertanding is that すしがほしいです is not a request, you are simply stating that you want sushi - perhaps your friend has asked you what you want to eat for lunch.
おすしをください is a polite request to be given sushi, perhaps if you are ordering in a restaurant (although I'd want to be more specific on what sushi in that instance!)
Osushi ga hoshii desu is not less polite than osushi wo kudasai - they are saying completely different things. Osushi ga hoshii desu means I want sushi. The honorific o is odd though. I have never used it and wouldn't use it. As for osushi wo kudasai it means Sushi please or Please "give me" some sushi - I've used speech marks because there is no verb saying "give" but that is essentially what you are saying. It is a polite command asking the listener to give you sushi. Both are polite - just saying different things. Impolite would be using the base 4 of a verb to order someone to give you sushi - sushi kure! It's basically the imperative (command) in plain form so super rude.
I was really taken aback by osushi meaning sushi, because of how it sounds. I've literally put my ear against my phone to get all the sounds out of it and it's like os'shi, instead of one sushi. There is no su sound to be heard. So is it normal for Japanese to say sshi instead of sushi?
I can hear the su fine. If anything the shi is faster and shorter than the su. It is perfectly normal and natural for words to blur together when people are speaking their native tongue, especially when speaking quickly or at a speed that might seem fast to non native speakers.
I never heard anyone say "I want sushi". It's always "I want some sushi".
おすしが ほしいです is a statement, not a request. This is why it is not rude and why please is not necessary. The speaker is not asking for some sushi, they're just stating that they'd like some sushi - you know, like when you say to your friends - man, I could really go for some sushi right about now. You're not saying please give me some sushi - you're stating that you want some.