1. Recent paper suggests that gamma-H2AX is not only a marker for DNA double-strand breaks but also the biomarker of the replication stress, which means that the accumulation of gamma-H2AX in the nucleus does not necessarily mean the DNA damage response.
2. p38MAPK is a stress responser to ROS, irradiation, inflammation etc, which means that p-p38-MAPK is not specific.
I agree with Matteo. I would like to add that an inclusion of p21 levels, along with p53 and p-p53 (Ser-15) levels, would be more reassuring that radiation had an effect on cells that expressed a functional p53.
A simple biochemical assessment of malonaldehyde should answer your question! But it is time dependent and depends on cell line/tissue used. You can also test the generation of free radicals like hydroxyl, superoxide, lipid peroxide etc. these experiments are less expensive and can be performed in any biochemical lab.
Very broadly, cell death, proliferation and DNA damage response (I mean here not only its phenomenological studies but also pertinent mechanistic studies) are assessed, but this depends on many things such as which endpoints you wish to look at, experimental systems (e.g., in vitro and/or in vivo), and types of radiation you use (e.g., sparsely ionizing, densely ionizing, or non-ionizing).