Oxidation state of tungsten in W3O8
Note that $\ce{W3O8}$ is a non-stoichiometric compound and it is not that simple compound you may think. It has a very complex structure as such its oxidation state is very difficult to calculate. I am not going in details about the structure of the compound and I will only mention it a non-stoichiometric compound actually a oxygen-deficient cluster. 

Please give a good read to Xin Huang et.al., J. Phys. Chem. A 2006, 110, 85-92, the link that @JM97 has posted. It says that the $\ce{O-O}$ is much longer than normal oxide bond and so it is assumed to be a peroxo bond $\ce{O2^2-}$. Now, peroxide has oxidation state of -1. So, assuming $\ce{W3O8}$ to be a simple compound (no stoichiometric defect or any kind of defect), the oxidation state is: 

$$3x + 8(-1) = 0$$
$$x = +{8/3}$$