"Is there an effective method for cleaning 5-gallon stainless-steel containers which are used to transport and store oil in our plant?"
Many companies prefer to use 5-gallon plastic buckets (also known as popcorn pails) because oil doesn't tend to stick but flows out readily and is easy to wipe down. Others use disposable, off-the-shelf plastic liners, similar to what is used in the food industry.
If you must use and clean stainless-steel buckets, you may need a standard parts-cleaner/degreaser, the kind mechanics use in garages and rebuild shops. Either petroleum or nonpetroleum-based solvents are preferred. The final cleanup is often with a common dishwasher using water and detergents. Filtered water is best.