Can MRI detect irritation/inflammation of the ilioinguinal and iliohypogastric nerves in the pelvis?

Yes it can. Electrophysiologic study is the standard way of checking for nerve entrapment. Lately, with the advent of new technologies, MRI & mr neurograpy can be used as diagnostic tools as well. Take care! http://m.Radiographics.Rsna.Org/content/30/4/983.Long.
May not . If the radiologist has enough clinical information he or she may find some contributing finding on the mri. The diagnosis for ilioinguinal and iliohypogastric nerve irritation/inflammation (usually due to entrapment) remains largely a clinical one, meaning an imaging modality can help support the diagnosis but a normal study will not rule it out.