Here's my take on the book:
Cover appears to be by Art Saaf - which I find odd as I don't think he's known to have worked there.
Help Me, Doctor is Sekowsky & an inker (a la Mike Peppe)
The Cop is Howard Nostrand (note the "Epp & Co" on the truck in splash panel)
Outside the Law is Sekowsky again, but with traces of Bill Draut? Dunno how or why HE should be there.
text illustration looks like Nostrand on the male and someone else (Gene Fawcett?) on the girl.
Luke the Spook - I don't know who this is. This style has been credited to Nostrand, but it isn't him. And I've seen it ID'ed as Howard Post, but it ain't him, either.
Hope that helps.
My 2