Bottom 木 - pictograph of a tree with branches and roots. Indexes 桨 in the wood family with 板 plank, 棒 stick, 桌 table. An oar is a long wooden shaft, so the radical does its job: 桨 = a wooden tool you grip and pull through water.
Top-left 丬 - three-stroke side form of 爿 'splint of wood.' Acts as the abbreviated phonetic root: 丬/qiáng + 夕 together form 将, the real phonetic of 桨. Same sound family in 浆 starch, 奖 prize, 蒋 surname Jiang - all share this 丬+夕 top.
Top-right 夕 - pictograph of a crescent moon, partner to 丬 in the simplified 将-top. Here it has lost its evening meaning and works purely as part of the fused phonetic block, carrying no semantic contribution beyond completing the standard 将-shape silhouette.