Ion-molecule reactions between clusters of H$_2$/D$_2$ and O$_2$ in liquid helium nanodroplets were initiated by electron-induced ionization (at 70 eV). Reaction products were detected by mass spectrometry and can be explained by a primary reaction channel involving proton transfer from H$_3$$^{+}$ or H$_3$$^{+}$(H$_2$)$_n$ clusters and their deuterated equivalents. Very little HO$_2$$^{+}$ is seen from the reaction of H$_3$$^{+}$ with O$_2$, which is attributed to an efficient secondary reaction between HO$_2$$^{+}$ and H$_2$. On the other hand HO$_4$$^{+}$ is the most abundant product from the reaction of H$_3$$^{+}$ with oxygen dimer, (O$_2$)$_2$. The experimental data suggest that HO$_4$$^{+}$ is a particularly stable ion and this is consistent with recent theoretical studies of this ion.