Can anyone just come into my Barracks room even after I say no?

Can your chain-of-command (below the unit Commander) do an informal walkthrough during your off-duty hours? No.

Can your unit Commander who is responsible for the barracks conduct an informal walkthrough during your off-duty hours? Yes.

Can your chain-of-command (below the unit Commander) do an informal walkthrough during your off-duty hours IF the Commander has delegated that authority to do so? Yes.

Bottom line: The Commander 'owns' the barracks and is the only one that can authorize entrance for formal or informal inspections of a "private" living area (put in quotes as it is technically "more private" than "public"). HOWEVER, Commanders usually delegate this (I always did) down to first line leaders (for informal inspections).

There is no restriction on WHEN or HOW OFTEN a Commander (or those he delegates authority to) can do inspections, however they will have to use their judgement on what is 'too lax' and what is 'too onerous' and starts to affect morale.

There is a difference between a "spot walkthrough" for general cleanliness/upkeep and a more formal health and welfare inspection. If the latter, then those have to be systemic and applied across the board throughout the unit and are usually scheduled (not 'announced to the unit') by the Commander.

Can they "just come into my room" to do "inspections"? Again, it depends. Is it an informal "Just doing a quick check on you" or is it a more formal "Health and Welfare"? Yes to the former and No to the later.

There will usually be a unit or installation policy (typically called a "Barracks Management Policy") that governs when walkthroughs/inspections can occur.

I don't know how long you've been with the unit, but when I was in, as a SP4, I was instructed by my section chief to do informal room inspections on the new guys. I wasn't to scream or discipline, just correct and report. Once we knew the new guy wasn't a slob, that stuff stopped.
On the obverse, I've seen some nosy barracks rats who just want to see what you got.

You said Spc and below, there are no leaders or supervisors in that group, unless the SPC is in an NCO billet and the Commanders policy allows First line sups to check healthy md welfare.

Bottom line is the should be a unit SOP on barracks inspections and walkthroughs. Again that is almost always delegated to the NCO support channel, but with specific guidelines your cello section mates have no business in your room.