Listen, the guy used the wrong term. A stage is an often misused term in the US--technically, a stage is someone who works for a period of time in a kitchen as a learning experience but for either no pay or subsistence pay (like they might hook you up with a bed to sleep in or something). This is what you would do if you were to, say, travel Europe for a few months and work for free in any number of kitchens that would have you.
What the chef MEANT to say was that he wanted to do a job tryout with you and make sure you weren't a complete buffoon on the line before hiring you. To make sure you gel with the staff, know what a hotel pan, 9th pan, etc all are. See some basic knife skills, help with prep, then maybe work next to a cook (likely on the station you are likely to work) and learn. If you do well, at some point in the night you will probably be asked to pick up a dish by yourself (under supervision) and show what you got.
There is absolutely NOTHING wrong with doing this--it is very standard in a lot of places. Chefedb means well, but I think he/she was under the assumption that this chef just wants you to go in and be free labor. Think of it more as a working job interview/tryout. It's totally, 100% normal and nothing to be upset about--it's unlikely that this chef uses the working interview for much free labor.
Also remember: you are interviewing them as well. This is a GOOD thing, because you will know pretty fast if this is a kitchen you could work in full time. If you see clean cooks, working hard, not TOO much grab-ass, people being serious about food, having standards, not cutting corners, etc, it's good. If you go into the kitchen and it's filthy, and the food sucks, etc, then you know it won't be right for you.
It's likely that you won't stay the entire night...you'll be let go once the rush is over, and then they will talk about you when you leave. Make sure you get a timeframe from the chef/sous chef about what the next step is--he might have a couple more people coming in, he might not, but try to get a firm "I'll call you by such-and-such date about the job" or you say "Chef, I'll call you on Monday to see where we stand" before you leave. This might make you feel better if it goes a couple of days with no word.
And no, don't wear a suit. Wear a clean kitchen uniform and sharpen your knives. Take your jacket on a hangar and bring a hat of some sort. Maybe an apron too (don't assume they have aprons). Make sure your shoes are clean, etc. IMO a suit would be way overkill...if it were a management position I would say otherwise but I highly doubt he will think more of you if you wear a suit (lol, maybe he'd think less).