You will find an answer to your question in Hatcher's book project "Vector bundles an K-theory" (p. 75-76) (available on his homepage). Using the fact that $\pi_8(O(10))=\mathbb Z_2$, you can build a non- stably trivial vector bundle over the sphere $S^9$ (using the clutching function associated to the non-trivial homotopy class $S^8\rightarrow O(10)$ representing the generator of in $\pi_8(O(10))$). This vector bundle has all his Stiefel-Whitney and Pontryagin classes equal to zero.
The vanishing of $w_9$ follows from Wu's formula $w_9=w_1w_8+Sq^1(w_8)$.
