  Very recently one has started to study Bergman and Szeg\"o kernels in the
setting of octonionic monogenic functions. In particular, explicit formulas for
the Bergman kernel for the octonionic unit ball and for the octonionic right
half-space as well as a formula for the Szeg\"o kernel for the octonionic unit
ball have been established. In this paper we extend this line of investigation
by developing explicit formulas for the Szeg\"o kernel of strip domains of the
form ${\cal{S}} := \{z \in \mathbb{O} \mid 0 < \Re(z) < d\}$ from which we
derive by a limit argument considering $d \to \infty$ the Szeg\"o kernel of the
octonionic right half-space. Additionally, we set up formulas for the Bergman
kernel of such strip domains and relate both kernels with each other. In fact,
these kernel functions can be expressed in terms of one-fold periodic
octonionic monogenic generalizations of the cosecant function and the cotangent
function, respectively.
