While Large Language Models have achieved state-of-the-art performance in general machine translation, they frequently struggle to adhere to complex stylistic nuances and lexical constraints strictly and often revert to a neutral style. The scarcity of style-specific parallel data hinders existing solutions, whereas standard prompting lacks rigorous verification mechanisms. To bridge this gap, we propose Style-Ruler, an inference-only agentic framework that operationalizes style via unsupervised extraction and neuro-symbolic verification. Style-Ruler orchestrates three specialized agents: (1) a Style-Reverse Analyst (SRA) that mines quantifiable linguistic constraints from monolingual reference texts via unsupervised extraction; (2) a Constraint-Adaptive Translator (CAT) that employs a Style-Chain-of-Thought mechanism to plan stylistic adherence before generation explicitly; and (3) a Sandbox-Augmented Auditor (SAA) that provides heterogeneous feedback through deterministic code execution. These components form a closed-loop refinement mechanism where symbolic logic guides neural generation. Extensive experiments on the GuoFeng Webnovel dataset and WMT24++ benchmark demonstrate the superiority of our approach. Style-Ruler achieves a CSR of 82.4% on stylized translation, surpassing standard Chain-of-Thought prompting by over 50%, while improving BLEU scores by +1.0 on En→Zh.