No ground wire???

Recently moved to a house built in 1961. When replacing outlets found that there's no ground wire, two wires only. Boxes are steel and I think there's metal conduit in there. Is ground provided by the screws holding the outlet in the box? Effective? I would assume only if the conduit is grounded?

Have a newer box with circuit breakers and a lot of Romex coming out but not to my two audio outlets.

Any comments or opinions would be appreciated. Considering having an electrician run a new line for audio (which wouldn't hurt in any case). I would be more comfortable with a separate copper ground wire. All y audio stuff is three prong.
Absolutely have an electrician run a new, dedicated line, or maybe two, just for audio. It usually cost less than $100, and is one of the best bang for the buck upgrades out there.

Use at least 12 gauge wire and 20A breakers, maybe 10 gauge if you wish. You could even put in some new receptacles while you at it. You could go with fancy, Furutech, Oyaide, etc., but even less expensive models like Power Ports will make a nice difference.

Those two outlets are most likely fed by BX cable. BX carries the ground on the outer sheath and enters the steel boxes. Get an outlet tester for a few bucks at Walmart. It has two leads black and red with a led on the end.. You stick them in the outlet and it will light up. Then stick the red lead into the right side and the black on the steel box and if it lights up then you have verified that the outlet is grounded. Now all you have to do is replace the old outlets. No rewiring would be necessary.
The metal jacket of the BX cable acts as a ground. Being in contact with the metal box, you can buy a "grounding wire", usually green with a threaded screw at one end, and screw that into the back of the box. Then buy your outlet of choice and hook the other end into the outlet ground terminal. Of coarse, if doing it yourself, don't forget to disconnect power to that circuit.

"Absolutely have an electrician run a new, dedicated line, or maybe two, just for audio. It usually cost less than $100, and is one of the best bang for the buck upgrades out there."

An electrician come out to you house and run 1 or 2 dedicated lines for less than $100.00? I would imagine the material alone would exceed that (depending on distance from panel box to audio outlets).
Using the BX shielding as your ground varies on building codes. The good thing is that if you have the shielding there and it's a home run to the box, you can ground it to the outlet on one end and the panel on the other. At a minimum consider using a GFI outlet in case this shield shorts somewhere...
As said above, if the metal box is grounded via the armor of the bx cable, you only need to install a "self-grounded" outlet. It will work without requiring the grounding pigtail attached to the box. A self-grounding outlet is a three-prong type that has a brass tab at one mounting hole that grips the mounting screw to guarantee ground contact. Even if the screw works loose, the outlet will still always be grounded to the box. No GFI necessary.

Self grounding receptacle:

Grounding via yoke to box contact:
Back in 1961 steel boxes were used for rough-in boxes along with 2 wire Romex. In this case the metal box would not be grounded. A quick look inside would reveal a Romex clamp with a screw in the middle of the clamp holding down the Romex in place. You should also see the outer sheath of the Romex extending into the box beyond the Romex clamp.

Steel box with Romex clamp.