Understanding the prevalence, disparities, and symptom variations of Post COVID-19 Condition (PCC) for vulnerable populations is crucial to improving care and addressing intersecting inequities. This study aims to develop a comprehensive framework for integrating social determinants of health (SDOH) into PCC research by leveraging NLP techniques to analyze disparities and variations in SDOH representation within PCC case reports. Following construction of a PCC Case Report Corpus, comprising over 7,000 case reports from the LitCOVID repository, a subset of 709 reports were annotated with 26 core SDOH-related entity types using pre-trained named entity recognition (NER) models, human review, and data augmentation to improve quality, diversity and representation of entity types. An NLP pipeline integrating NER, natural language inference (NLI), trigram and frequency analyses was developed to extract and analyze these entities. Both encoder-only transformer models and RNN-based models were assessed for the NER objective. Fine-tuned encoder-only BERT models outperformed traditional RNN-based models in generalizability to distinct sentence structures and greater class sparsity. Exploratory analysis revealed variability in entity richness, with prevalent entities like condition, age, and access to care, and underrepresentation of sensitive categories like race and housing status. Trigram analysis highlighted frequent co-occurrences among entities, including age, gender, and condition. The NLI objective (entailment and contradiction analysis) showed attributes like "Experienced violence or abuse" and "Has medical insurance" had high entailment rates (82.4%-80.3%), while attributes such as "Is female-identifying," "Is married," and "Has a terminal condition" exhibited high contradiction rates (70.8%-98.5%).