Depo Medrol is an injectable steroid (think contisone). The typical side effects include increase in the amount of water the dog drinks (and thus increased need to urinate more frequently) and increase in hunger. Depending on the dose, the dog tends to "feel good" and if used long term and in high doses can cause ulcers, especially in the mouth.
This steroid is often used for dogs with flea allergies, but as with any steroid, long term or freqent use is generally not a good thing. It is better to address the cause of the problem. Long term treatment is generally restricted to immune diseases.