Can dryers can be wired directly into electrical supply instead of an outlet?
Yes, you can hardwire a dryer or stove to that wire. They always used to be done that way and still could be unless code forbids it where you are. But it's really best to have an outlet instead, and new appliances come with plugs on them now. Makes it far easier if you ever need to disconnect the appliance for any reason because all you have to do is unplug instead of shutting off the power, disconnecting it all, and doing the reverse later, and gives you much more freedom to move them out to clean behind them. A dryer will take a four prong outlet because it has a 220 volt supply.
Yes, it's possible to wire some dryers w/o a plug. However, it's not commonly done in residential settings as most people don't have an electrician around to disconnect it if it needs service or to be moved for some reason.
It would depend on your areas electrical code if it was legal to do that or not. I cannot see why in a residential setting anyone would need to do that. If I were you I would call an electrician to check the wires and install a proper outlet.