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You will not be able to collect your bags, as there is no airside baggage claim in Oman.
At some airports (like Dubai), there is a (premium - ie, paid) service for transit passengers that allows staff to collect bags and re-check them in for the next flight - but this depends entirely on the airlines involved as some do not allow this.
At Muscat International Airport, the lounge services are provided by Plaza Network; they offer "baggage services" (but no further details are provided on their website). They can also assist with your transit visa.
As you cannot select your final in-bound flight; I would recommend contacting the lounge operator to see if they can assist, or at minimum - get them to assist you with the transit visa so you can collect your bags and re-check them for your final leg.