Can I use 1 to 2 power adaptor to measure current with multimeter

No, that one will only allow you to measure voltage due to parallel connection. Your current shunt (multimeter) needs to be in series to measure current.

Commercial breakout boxes does exist for the very purpose you are describing and there are multimeter accessories too. Here are some examples:

How much accuracy do you need? Would a normal plug in power meter suffice?

No this is not possible with a standard multi-outlet adapter. They are wired so that all outlets are in parallel. So you could measure voltage but not current, as you need a series connection to measure current.

There are specialized measurement adapters available which allow you to measure both, current and voltage and with the right tools you can measure power then.

No, you can't. If you connect a multimeter on amps range to the adaptor then it will go bang as you short out the supply.

An ammeter needs to be in series with the load. Or else use a clamp meter clamped around only one of the live or neutral wires.