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© 2016 American Physical Society. J. L. B. S., J. K. and S. M. gratefully acknowledge support by the DFG Research Training Group 1620 Models of Gravity, as well as support from FP7, Marie Curie Actions, People, International Research Staff Exchange Scheme (IRSES-606096). J. L. B. S., L. M. G. R., J. K. and F. N. L. gratefully acknowledge support from MINECO, under research Project No. FIS2011-28013., We investigate axial quasinormal modes of realistic neutron stars in Einstein-Gauss-Bonnet-dilaton gravity. We consider eight realistic equations of state containing nuclear, hyperonic, and hybrid matter. We focus on the fundamental curvature mode and compare the results with those of pure Einstein theory. We observe that the frequency of the modes is increased by the presence of the Gauss-Bonnet-dilaton, while the impact on the damping time is typically smaller. Interestingly, we obtain that universal relations valid in pure Einstein theory still hold for Einstein-Gauss-Bonnet-dilaton gravity, and we propose a method to use these phenomenological relations to constrain the value of the Gauss-Bonnet coupling., Unión Europea. FP7, Ministerio de Economía y Competitividad (MINECO), DFG, Depto. de Estructura de la Materia, Física Térmica y Electrónica, Fac. de Ciencias Físicas, TRUE, pub