We applied natural language processing and inference methods to extract social determinants of health (SDoH) information from clinical notes of patients with chronic low back pain (cLBP) to enhance future analyses of the associations between SDoH disparities and cLBP outcomes. Clinical notes for patients with cLBP were annotated for 7 SDoH domains, as well as depression, anxiety, and pain scores, resulting in 626 notes with at least one annotated entity for 364 patients. We used a 2-tier taxonomy with these 10 first-level classes (domains) and 52 second-level classes. We developed and validated named entity recognition (NER) systems based on both rule-based and machine learning approaches and validated an entailment model. Annotators achieved a high interrater agreement (Cohen's kappa of 95.3% at document level). A rule-based system (cTAKES), RoBERTa NER, and a hybrid model (combining rules and logistic regression) achieved performance of F1 = 47.1%, 84.4%, and 80.3%, respectively, for first-level classes. While the hybrid model had a lower F1 performance, it matched or outperformed RoBERTa NER model in terms of recall and had lower computational requirements. Applying an untuned RoBERTa entailment model, we detected many challenging wordings missed by NER systems. Still, the entailment model may be sensitive to hypothesis wording. This study developed a corpus of annotated clinical notes covering a broad spectrum of SDoH classes. This corpus provides a basis for training machine learning models and serves as a benchmark for predictive models for NER for SDoH and knowledge extraction from clinical texts.