Would a single depmedrol shot for allergic asthma have less side effects than taking oral steroids?

Not particularly: When you take a depot shot you are taking a steroid in a dispensing medium that permits gradual release of the drug over a long duration. In many respects it equates to taking an oral steroid over several days. There are calculations that can be made if the actual drugs/amounts are provided. The way to avoid most side effects is the inhaled steroids that work & are broken down in the lung.