Hi,
Here is the step by step procedure to find the answer:
First of all we need to find out the molecular mass of H2SO4
-  H = 1.008
-  S = 32.065 
- O = 16 
So mass of H2 SO4 will be : (2x1.008) + (1x32.065) + (16x4)
 = 98.081 g/mole 
 This shows that 1 mole of H2So4 contain 98 grams.
Now we need to fin out the no. of moles of H2SO4 in 250 grams
 250 g x (1mole/250g) 
 = 2.5489 moles
 Now we need to find out how many moles of oxygen are present in 2.5489 moles of H2SO4.
So, as mentioned in the formula of H2SO4, we can see that four moles of oxygen are present in one mole of H2SO4
It means that 2.5489 moles of H2SO4 contain:
 2.5489 x4 
 = 10.19565 moles of oxygen 
Now, it is very simple to determine the mass of 10.19565 moles of oxygen by using the formula:
 no. of mole= mass/molar mass
 10.19565 moles= X/ 16 g
 10.19565 x 16= X
 X= 163.13 grams 
 Therefore, mass of oxygen in 250 g of H2SO4 is 163.13 grams 
 Hope it help!