Well the resulting solution will have carbonate ions, strontium ions, and acetate ions.
Isolating just the strontium acetate would take a little more work. Should be easy enough neutralizing the carbonate with hcl then dropping out the salt.
No oxygen. It just goes out as CO2. Same as making a volcano with baking soda and vinegar.
No time to calculate, so try this yourself and I'll come back after work. Figure the number of moles of strontium carbonate. You need that many moles of acetic acid plus maybe 10% or so to make sure it goes all the way.
SrCO3 has a molar mass of 147.63. So in 1g you have about 0.00677 moles. Let's just call it 7 mmol of Sr.
So you need about 14mmol of acetic acid. Let's leave some wiggle room and shoot for 16mmol. There will be a little bit of acetic acid left over but it shouldn't be much.
Acetic acid has a molecular mass of 60g/mol. So 16mmol is 0.96g of acetic acid.
Glacial acetic (that's still what you've got right?) is almost pure acetic acid and has a density very near to 1g/ml. I think if you want to use 1ml of acetic for 1g of SrCO3 you should come out just about right.
Be careful, it may very well fizz and pop. I think I would put 10ml or so of water on top before I started adding acid just to be on the safer side. As you stir in the acid (slowly) the SrCO3 should dissolve and bubble. The resulting solution will be about 0.7M in Sr(OAc)2. You can run that calculation out to get a more exact number if you want. If you're not sure, then post it here and I'll check it for you.