Bio-inspired underwater vehicles could yield improved efficiency, maneuverability, and environmental compatibility over conventional propeller-driven underwater vehicles. However, to realize the swimming performance of biology, there is a need for soft robotic swimmers with both distributed muscles and kinematic feedback. This study presents the design and swimming performance of a soft robotic fish with independently controllable muscles and embedded kinematic sensing distributed along the body. The soft swimming robot consists of an interior flexible spine, three axially distributed sets of HASEL artificial muscles, embedded strain gauges, a streamlined silicone body, and off-board electronics. In a fixed configuration, the soft robot generates a maximum thrust of 7.9 mN when excited near its first resonant frequency (2 Hz) with synchronized antagonistic actuation of all muscles. When excited near its second resonant frequency (8 Hz), synchronized muscle actuation generates 5.0 mN of thrust. By introducing a sequential phase offset into the muscle actuation, the thrust at the second resonant frequency increases to 7.2 mN, a 44% increase from simple antagonistic activation. The sequential muscle activation improves the thrust by increasing 1) the tail-beat velocity and 2) traveling wave content in the swimming kinematics by four times. Further, the second resonant frequency (8 Hz) generates nearly as much thrust as the first resonance (2 Hz) while requiring only $\approx25$% of the tail displacement, indicating that higher resonant frequencies have benefits for swimming in confined environments where a smaller kinematic envelope is necessary. These results demonstrate the performance benefits of independently controllable muscles and distributed kinematic sensing, and this type of soft robotic swimmer provides a platform to address the open challenge of sensorimotor control.