高校になってからは、クロスカントリースキー、ノルディック複合競技の大阪大会および近畿大会で幾度となく優勝。

、、。

Once he got to high school, he won any number of titles in the Osaka and Kinki regional championships in cross-country skiing and Nordic combined.

Literal

High-school became [after-てから topic-は], cross-country-skiing, Nordic-combined event [attributive-の] Osaka competition [and-および] Kinki competition [in-で] number-of-times-beyond-count-[幾度となく] won.

A sports biography sentence. 高校になってから ('once he got to high school') is the set temporal. 幾度となく ('any number of times, countlessly') is a literary set phrase — 幾度 ('how many times') + と + なく ('without') combined to mean 'without being a specific number, many times.' 及び ('and,' formal) links the two competition names. ノルディック複合 ('Nordic combined') is the skiing event combining cross-country and ski jumping.