Bear in mind that these devices can take a hefty current when loaded. If it's not designed to be plugged into a lighter socket, it probably needs a dedicated feed from the battery to be safe. Interior light feeds and the like are not designed to take this sort of current.
As with a supply to an audio amplifier, work out the maximum current draw, get some cable that's up to the job and run a positive feed from the battery, with a fuse protecting the circuit as close to the battery as possible. The negative supply connection to the inverter can be made to the vehicle body at a convenient point close to the fitted location.
150 watts at 12 volts is over 12 amps, and a lighter socket is normally rated at about 10. This assumes that the inverter is 100% efficient, which they're not, of course, so the actual current will be 15 amps or more.
Anything bigger certainly needs a dedicated circuit installing.
Having said this, a charger for a power tool is probably only going to take a few tens of watts, so it doesn't need to be a large inverter.
If you need it to switch off with the ignition, fit a relay in the circuit capable of taking the expected load and connect the coil to an ignition switched feed.
Kevin