Amblyopic and strabismus subjects experience inter-ocular suppression, impaired stereoacuity, and increased fixation instability. The purpose of the study was to investigate factors affecting suppression and stereoacuity and examine their relationship to fixation eye movement (FEM) abnormalities. We recruited 14 controls and 46 amblyopic subjects (anisometropic = 18, strabismic = 14, and mixed = 14) and 11 subjects with strabismus without amblyopia. We utilized the dichoptic motion coherence test to quantify suppression, and stereoacuity was assessed using the Titmus Fly test. We recorded FEMs using high-resolution video-oculography and classified subjects that did not have nystagmus (n = 27) versus those with nystagmus (n = 32; fusion maldevelopment nystagmus [FMN], n = 10) and nystagmus that did not meet the criteria of FMN (n = 20). We also recorded FEMs under dichoptic viewing (DcV) at varied fellow eye (FE) contrasts and computed the amplitude and velocity of the fast and slow FEMs and vergence instability. Inter-ocular suppression and stereoacuity deficits were closely correlated with an amblyopic eye (AE), visual acuity, and strabismus angle. Subjects with nystagmus displayed more pronounced stereoacuity deficits than those without nystagmus. Strabismic subjects with and without amblyopia, who demonstrated a fixation switch at 100% FE contrast, had lower inter-ocular suppression than subjects lacking a fixation switch under DcV. Amplitude of fast FEMs and velocity of slow FEMs, and vergence instability were increased as the FE contrast was lowered in both amblyopic and strabismic subjects. The current study highlights the intricate relationships between AE visual acuity, eye deviation, and FEM abnormalities on suppression and stereoacuity deficits and underscores the need to evaluate FEM abnormalities while assessing dichoptic treatment outcomes.