If you run an amp through a resistance of an ohm, a volt of potential is created. So voltage, current, and resistance are not independent things. It makes no sense to say that current alone is deadly or that voltage alone is deadly. For some reason people say current is the dangerous one even though that statement directly contradicts Ohm's Law.
A watt is a joule of energy every second. The more watts your waffle iron puts out, the faster your waffles will cook.
However, none of these things are fundamentally dangerous. There are a lot of misconceptions about this. Energy (joules) is dangerous. If you put a wooden spoon on 1,000W an electric stove for half a second and nothing will happen. Only a small amount of energy was transfered into the spoon. Do it for an hour and your house will burn down. Touch a 500kV high tension wire for a picosecond and nothing will happen. Grab it for a minute and you'll be long vaporized.
So energy is the dangerous one. Power (watts) is the rate of energy transfer. Voltage and current are the factors that together allow energy to be transferred. Voltage times current is wattage. You need both current and voltage to transfer energy. But it is a physical law that energy is not created or destroyed. Thus voltage and current can only cause the transfer of whatever energy is available to the system. When that energy is depleted, voltage and current will both drop to zero.
This means that doorknobs, which can store tiny static charges, are far less of a concern than wires connected to a nuclear power plant. The common misconception is that 100 mA is deadly. However, it's not unreasonable for a doorknob to be charged to 5000 V relative to you after you slide your house slippers across the carpet. Your skin is about 5000 ohms. So that means a doorknob will cause 1 A to flow through your body, 10 times the supposedly deadly amount. But since doorknobs only have a small amount of energy to transfer, that 1 A and 5000 V drops exponentially to zero so quickly that there is no danger at all. The wires connected to the power plant supply essentially unlimited energy and so you would die if you held onto a 5000 V wire coming from a power plant.
As far as fire, that's all about resistance. Resistance creates heat when you transfer energy through it. Some of the energy gets lost in the resistance and the heat is the energy that doesn't make it through that resistance. A requirement for fire is that there be enough energy in the first place to start a fire. This energy requirement depends on the conditions. A doorknob shock can start a fire in a room full of gasoline fumes. Overloaded circuits can burn through their insulation and the wood studs in a wall. An overloaded circuit is one that's being used to transfer too much energy through too great a resistance. Thus heat is being produced--the wires in the walls heat up. That can start a fire.
High voltage can also start fires because it can push current, and thus energy, through unexpected resistances. Normally, the insulation in your house wiring is resistive enough to keep all the energy inside the wire. Jack the voltage up to 1,000,000V, say in a lightening strike, and huge amounts of energy is going to be going all over the place. Then you'll have a fire.