I noticed that I was getting hum/noise from some of my outboard gear
As others have remarked, there are many possible sources for this him.
The suggestion of running a FFT (I use Wavegene and Wavespectra among other software) and then chasing the problem down to individual cables and devices by adding Device after device is spot on.
It is also useful to observe the spectrum of the noise, which can give hints regarding the source.
Hum dominated by 50/60 Hz is from mains (and usually earth loops), while 100/120Hz dominated hum usually indicates a power supply problem, either a fault from aging or a design flaw.
Some hum/noise came from my DIY outboard which I built with ground lift switches on them but they didn't reduce or stop any hum/noise when I toggled them.
This suggests the problem is not caused by an earthloop on this device.
I was reading online that having all my gear plugged into one power socket could be a solution
The solution depends on the problem. Using a single wall socket from which all equipment is powered via extension vmcables, long cables etc. certainly reduces some specific problems.
I am concerned that it may put a strain on one socket having all the equipment plugged that way?
Check the current ratings of the equipment and add up, or better measure it using one of these plug in power meters used on household appliances to find vampire loads and power hogs to bring down the electricity bill.
Add everything up. Usually main sockets are good for well over 10A which in the USA is over 1kW and in Europe and other 230V countries 2kW.
Be careful with cheap Chinese extension cables and distribution boards. Don't be a Wallmartian.
It may be worth to make a diy project of a mains distribution Unit (or more than one) using preferably neutrik powercon connectors (otherwise for USA and USA voltages use "hospital grade" outlets), extra heavy star wired Earth connections and Filter units for sockets equipment with switched mode power supplies is plugged into.
Make your own powercon mains cables and plan for a cascading set of distribution units. Mains cables should low contact resistance connectors (again, powercon scores big) and low resistance earth connections.
These can help get a few extra dB in noise reduction from ground/earth loops which are essentially unavoidable if equipment is used in a complex audio system while using equipment in compliance with electrical.safety regulations.
For extra credit, you can make an isolated balance power system, if all you are running is low powered gear, 500VA transformers with dual 55V secondary windings are commercially available. Only drawback, all gear must be able to run on 110V.
The benefit is that with the power supply now 55-0-55V you are operating everything at what is classed as "safe extra low voltage" in most applicable ordinances, laws et al.
This means you no longer need to comply with electrical safety regulations for mains powered equipment and you lift the safety earth connections (as one example) to your hearts content.
I read that using a UPS could be a possible fix so that I isolate the outboard gear and help stop the ground loop from happening.
Unlikely, a UPS must follow electrical safety rules, it could only help if the UPS is disconnected from the wall and supplying power from it's battery, which is usually accompanied by a lot of fan noise, is not very efficient and inconvenient. Never mind the risk of the unit having run flat in the middle of the perfect take.
It may still be worth adding a UPS if power outages and/or brownout are common.
Is there generally a rule on how you group your equipment to the-same power source to prevent hum/loop noise?
Yes. Starbearth for both safety and low noise. Minimum loop impedance for earth connections from equipment to outlet and between outlets.
But I suggest to first isolate and diagnose the problem before running around for solutions. The problem may very different from what you think.
When I read "tube ...." and especially if a little aged, then I'd first suspect Power supply issues. Modern standards and expectations for hum and noise differ notably from the 1960's.
Thor