The Yukawa one-component plasma (YOCP) is a versatile model relevant to many strongly coupled laboratory systems including complex plasmas and colloids. In this work, the structural and thermodynamic properties of YOCP liquids are computed via four advanced integral theory approaches. Considering both accuracy and computational speed, the isomorph-based empirically modified hypernetted-chain approach is identified as the most promising alternative to computer simulations for the calculation of the YOCP static properties.