at.algebraic topology - Oriented Cobordism Rings

There is no torsion other than 2-primary torsion in the oriented bordism ring. One has that after inverting 2, the oriented bordism ring is a polynomial algebra on generators in degrees which are multiples of 4:
$$
Omega^{SO}_*[1/2] = mathbb{Z}[1/2, x_4, x_8, x_{12}, ldots]
$$
If I remember correctly, this (and the answers to many bordism-related questions) can be found in Stong's "Notes on cobordism theory".