The “riser group structure—fluid between risers” is taken as the carrier, and the “three-riser system” is selected as the research object, the experiment on the vortex-induced vibration of a three-riser group coupling interference effect is performed with variable angles between the riser group and the incoming flow, and the angles are 0°, 30°, 45°, 60° and 90°. Adjacent risers are arranged at the spacing of 4 times the diameter, and the external flow changes within 0.1–0.6 m/s. Based on the strains obtained by the fiber Bragg grating sensors and the modal decomposition theory, the concepts of “frequency interference ratio” and “displacement interference efficiency” are introduced to analyze the dynamic characteristics and dynamic response evolutions of the riser group at different incidence angles. The correlation of displacement along the riser when modal competition occurs to risers is explored, and the nonlinear effect of the external flow coupled with the wake and gap flow on the structure is researched. The results indicate that the wake shadowing effect constitutes the main constraint of the midstream and downstream risers at angles 0° and 30°, which leads to the gradual reduction of the Strouhal numbers and the sudden reduction in the dominant frequencies of the midstream and downstream risers at 0°. The boundary effect is mainly reflected in the 45°-, 60°-, and 90°-riser groups, which increases the vibration frequency. The interference effect of wake and gap flow on the variable-angle riser group causes the intensity of the mode transition to be different, and the deflection of the vibration trajectory in the 45°-riser group causes the displacements in both directions to approach. Crucially, the dominant frequencies represented by the Strouhal numbers peak, and the displacement mode transition represented by the traveling wave characteristic maximize both at 60°. The frequency interference ratio and displacement interference efficiency are not exactly consistent, and the interference effects in the in-line and cross-flow directions are significantly different. For a variable-angle riser group, cross-flow displacement under high velocities would be the key consideration in engineering design, and its interference effect on the riser group at low velocities is not negligible, either.