Recently, we have proposed a nutrient-limited model for the avascular growth of tumors including cell proliferation, motility, and death [S. C. Ferreira, Jr., M. L. Martins, and M. J. Vilela, Phys. Rev. E 65, 021907 (2002)], which qualitatively reproduces commonly observed morphologies for carcinomas in situ. In the present work, we analyze the effects of distinct chemotherapeutic strategies on the patterns, scaling, and growth laws obtained for the nutrient-limited model. Two kinds of chemotherapeutic strategies were considered, namely, those that kill cancer cells and those that block cell mitosis but allow the cell to survive for some time. Depending on the chemotherapeutic schedule used, the tumors are completely eliminated, reach a stationary size, or grow following power laws. The model suggests that the scaling properties of the tumors are not affected by the mild cytotoxic treatments, although a reduction in growth rates and an increase in invasiveness are observed. For the strategies based on antimitotic drugs, a morphological transition in which compact tumors become more fractal under aggressive treatments was seen.