We continue our studies on Riesz-type families of summability methods for functions and sequences, started in (Proc. Estonian Acad. Sci., 2008, 57, 70–80) and (Math. Model. Anal., 2010, 15, 103–112). Strong summability methods defined on the basis of a given Riesz-type family {Aα} are considered here. Inclusion theorems for these methods are proved. Our inclusion theorems allow us to compare the summability fields and speeds of convergence. The strong summability methods are also compared with ordinary summability methods Aα and with certain methods of statistical convergence. The proved theorems generalize different results that have already been published and are applied, in particular, to Riesz methods, generalized integral Nörlund methods, and Borel-type methods.