How does leukemia affect your lymph nodes?

It depends. It depends on the type of leukemia. All leukemias affect your immune system, because leukemia is abnormal growth of white blood cells. In acute leukemia, the tumor cells grow in the blood and usually the lymph nodes aren't enlarged. In chronic leukemia, (cll or cml) the lymph nodes can become enlarged from leukemia cells growing within.
Enlarges them... Leukemia is a form of cancer of the white blood cells (wbc). Wbc's are "processed" and stored in the lymph nodes. If they are cancerous and replicating rapidly, they will enlarge the lymph nodes.