We present muon-spin rotation/relaxation and susceptibility measurements on polycrystalline samples of EuL₂O₄, where L is the lanthanide Yb, Lu, Gd, or Eu. The magnetic phase of these quasi-one-dimensional zigzag chain compounds is characterized with respect to the difference in their lanthanide magnetic moment. We find that the magnetic phase varies systematically with the lanthanide magnetic moment. At zero lanthanide moments (EuLu₂O₄), we find a static antiferromagnetic phase; as the moment increases, the phase gradually changes to an incommensurate spin-density-wave ordered phase, and finally reaches a dynamic phase, when large lanthanide magnetic moments are present (EuGd₂O₄).