Ion irradiation is a powerful tool to tune properties of semiconductors and, in particular, of gallium oxide (Ga2O3) which is a promising ultra-wide bandgap semiconductor exhibiting phase instability for high enough strain/disorder levels. In the present paper we observed an interesting interplay between the disorder and strain in monoclinic β-Ga2O3 single crystals by comparing atomic and cluster ion irradiations as well as atomic ions co-implants. The results obtained by a combination of the channeling technique, X-ray diffraction and theoretical calculations show that the disorder accumulation in β-Ga2O3 exhibits superlinear behavior as a function of the collision cascade density. Moreover, the level of strain in the implanted region can be engineered by changing the disorder conditions in the near surface layer. The results can be used for better understanding of the radiation effects in β-Ga2O3 and imply that disorder/strain interplay provides an additional degree of freedom to maintain desirable strain in Ga2O3, potentially applicable to modify the rate of the polymorphic transitions in this material.