Does Murphy's oil soap kill bedbugs?

yes. any kind of soap would kill bed bugs. The way to do is to dissolve the soap in water & spry directly to the bug & its eggs.

you will see the bug dying.

That might kill the few that you see, But there are a hell of alot more hiding thru your whole house, They can spray poisons and throw away certain things BUT that wont get them ALL!! The ONLY way to kill them ALL is to close all the Windows and doors then have a huge fan IF you have a basement in the door way of the basement and one at the front door, Then put one of them heaters that look like jet engines behind it, Why you ask?? Bedbugs cant survive to high of a temp, If you can get it to I THINK around 135 F they will all die, But it cant be for a few mins you have to get your house to that temp and have it like that for a few hours or even better a whole day, Of course anything thats alive take out of the house, Thats the only true way to get rid of them ALL!! cuz heat will get into every part of the house cuz poisons cant get everywhere