By using two inequalities due to Hölder and Hardy, Littlewood and Polya as well as averaging functions, several interval oscillation criteria are established for the second-order quasi-linear differential equation with forced term of the form (r(t)y^′(t)^α−1y^′(t))^′+p(t)y^′(t)^α−1y^′(t)+q(t)y(t)^β−1y(t)=e(t) that are different from most known ones in the sense that they are based on the information only on a sequence of subintervals of [t₀,∞), rather than on the whole half-line, where β>α>0. Our results make use of the oscillatory properties of the forcing term and extend a recent result which is obtained by means of a Picone identity.