How prevalent was torture by the regular police force and the army in 19th and early 20th century in the US and Western Europe? When it was practiced, are there documented instances of it being effective?
You didn't define "torture" so it's very hard to answer.
One example would be Wickersham Commission report in 1931. While its main focus was avoidance of Prohibition and the latter effect on society, it also produced an infamous critique of the use of violent interrogation.
A lot of examples from early 1900's are listed in "Above the Law: Police and the Excessive Use of Force" by Jerome H. Skolnick, James J. Fyfe.
Torture is best and most effective in getting immediately verifiable information and as a tool in the fear arsenal of an organisation. The SS and Gestapo used it to great effects during the Nazi regime. Those are well documented in any history books. Note that Russia and the Soviet Union used torture as well as part of its repression and control methodology but arguably is not in "Western Europe". The East German Stasi used torture on a similar model to the Soviet.
What torture is not effective at is to give you long term intelligence on an organisation that the victim belongs too. Too much bias enter the questioning making it useless. However, fear of torture (or rendition) may prompt the suspect to be more cooperative.
Note on terminology: I have seen "showing female breasts to a prisoner" defined as torture. Many interrogation techniques used by Police forces could be described as coercion or torture depending on your agenda. Some things, everyone will agree are torture: electric shocks for example.