Background: Several studies have reported alarming rates of mental health issues and sleep problems among nurses even in the post-pandemic era. Objectives: To investigate the prevalence of stress, anxiety, depression, burnout and insomnia among nurses in Greece one year after the end of the pandemic and to construct a mediation model evaluating the impact of stress on insomnia, the chain mediating roles of depression and burnout, as well as the moderating role of anxiety in the model. Methods: This cross-sectional study was conducted online in July 2024 and included 380 hospital nurses who completed the Depression Anxiety Stress Scale (DASS-21), the Copenhagen Burnout Inventory (CBI) and the Athens Insomnia Scale (AIS). Results: The prevalence rates of stress, anxiety, depression, burnout and insomnia were 33.9%, 33.3%, 35%, 46.8% and 56.1%, respectively. Multiple regression analysis indicated that the Depression subscale of the DASS-21 explained 40.6% of the variance in AIS, while an additional 7.6% was explained by CBI and another 1.3% rate by the Stress subscale of the DASS-21. Mediation analysis revealed that stress affected insomnia both directly and indirectly through the chain mediating roles of depression and burnout. Anxiety moderated the chain mediation path by enhancing the negative impact of stress on depression. Conclusions: The proposed moderated chain mediation model introduces certain factors influencing insomnia and explains how changes in any one of these factors effectuate changes in the other factors, offering insights for individualized interventions.