Naval Radar in WWII was pretty dicey stuff. Low probability of detection of surface targets, no IFF systems, limited discrimination. Not good for observing and backtracking incoming fire, either.
Without the sonar, surface contacts were just a range and bearing. Good enough to shoot at, not good enough to justify shooting.
Essentially, all surface radar was "Bad"... just a matter of how bad.
I would suggest that you do some reading on the later night battles in the Solomon Islands campaign, in particular the Battle of Vella Gulf, where a US destroyer division sank three Japanese destroyers by torpedoes fired under radar control. Then I would suggest reading about the Battle of Surigao Strait, part of the Battle of Leyte Gulf, which was entirely a night surface engagement. The Battle of Empress Augusta Bay would also prove fruitful to read about.
Also worth reading are the accounts of the night engagements between the British Navy and the Italian Navy in the Mediterranean, and then there is the Battle of North Cape, occurring on December 26, 1943, where the HMS Duke of York sank the German Scharnhorst with the assistance of British cruisers and destroyers. This occurred well to the north of North Cape, Norway, where there is a singular lack of daylight at that time of year. Norman Friedman's book,
Naval Radar, has an excellent discussion of the development of naval radar during the World War 2 period, and is well worth the read.
As for sonar, during World War 2, it was limited to range and bearing only, with depth determination being estimated by the distance at which the contact was lost, and until the very end, when the US began to introduce a 360 scanning system, was basically a searchlight only unit. Norman Friedman's book,
US Naval Weapon Systems, has an extended chapter on US sonar development and World War 2 system capability. Norm autographed my copy. W Hackmann,
Seek & Strike: Sonar, anti-submarine warfare and the Royal Navy 1914-54, HMSO, London, 1984, is an excellent history of the development of British sonar during World War 2.
Additional data on the development of radar during World War 2 is available in the US Army official history of the Signal Corps during the war. The Signal Corps was the US agency in charge of radar development. The volumes can be downloaded from the Center for Military History, and are in searchable, copy and paste, PDF files.
http://www.history.army.mil/html/bookshelves/collect/ww2-ts.html
The following three publications are available for download from HyperWar.
The publication "U.S. Radar - Operational Characteristics of Available Equipment Classified by Tactical Application", short title FTP 217, is issued for the guidance of those concerned in planning of future operations.
http://www.ibiblio.org/hyperwar/USN/ref/Radar/index.html
US Night Fighter Radars of WW II
http://www.ibiblio.org/hyperwar/USN/ref/NightFighterRadars/index.html
The AN/APS-6 Pilot's Manual. This is a downloadable PDF file.
http://www.ibiblio.org/hyperwar/USN/ref/NightFighterRadars/APS-6PilotsManual.pdf
I would be remiss if I did not recognize our British Allies' contribution to the development of radar, which is covered in the following volume.
THE DEFENSE OF THE UNITED KINGDOM, By Basil Collier
http://www.ibiblio.org/hyperwar/UN/UK/UK-Defence-UK/index.html
The book by Bill Gunston,
Night Fighters, is also very useful in its discussion of night fighter operations from World War One on, and has a lot of useful diagrams of the various radar displays used during World War 2.
The US Navy's Office of Naval Intelligence Combat Narratives are also quite useful for looking at radar use in World War 2. Some of them are available on HyperWar at the following link. They can also be obtained directly from the US Navy.
http://www.ibiblio.org/hyperwar/USN/index.html
I should note that I own all of the books in hard cover, and have downloaded all of the digital files, so that I am only recommending what I have read and view as useful. I would imagine that forum users in the US should be able to obtain all of the books via interlibrary loan. British Forum members should be able to obtain most of them the same way, as Norm's books were also published by Conway Maritime Press in the UK.