What size tank less water heater would I need for a 3 bedroom, 2 bath house with 4 people living in it?

Tankless water heaters are sized in Gallons per minute. There are several good sizing guides on the web.

It would seem that for 2 tubs (4gpm) and 1 sink (1gpm) and a dishwasher (1gpm) a minimum size would be 6gpm. But that is the LOW side. Move up to 9gpm and you will probably never run out of hot water.

Note that you only want to go with LP or gas when doing a whole house tankless water heater. electric tankless would run higher electrical bills than a conventional electric hot water heater just to get the water hot enough for the high flow rates.

And yes they DO make exterior tankless hot water heaters.

=== suggest you get the largest tankless that you can fit into your budget .. four people and cooking and clean-up takes a bunch of hot water .... cover the outdoor h2o heater so you can slow down the rusting factors ... the bigger cover the better ....

no such thing as an outdoor tankless unit. they can be installed in basements or garages. you will need a fairly large capacity unit. check with local water utility about hard water- if it is hard, you will also need a tankless with a filtration unit attached <fairly small.> most tankless water heaters are smaller than a microwave.