EDIT: I just realized I had forgotten to point out that the electrical sockets in this crappy apartment aren't in fact even grounded except in the kitchen and bathroom. Since they're pretty much hidden away and I just deal with power strips, I didn't think of that before now. How does this affect dealing with the issue?
Jeez, how old is this electrical installation? In the US, grounded outlets have been mandatory in new buildings since the early 1970s (and that was later than e.g. in the UK and Germany). One would think that the last 50 years should have been enough time to bring things up to code.
Technically, you aren't even supposed to operate IEC Class I equipment without a proper ground. Electrical safety is only ensured when the wall outlet is replaced with a GFCI-equipped one (do you have those at least?), and even then multiple devices on one outlet strip in particular may still provide enough mains leakage to give you a noticeable tingle when touching a metal case.
The article
Cheater plug is a good read in this context.
This situation may be one step forward and two steps back. You may be able to avoid "hard" ground loops (by using multiple outlet strips) but may have fun with "soft" ones, plus the latent safety issues. If device ground is floating near half the mains voltage, open inputs also have a tendency to hum pretty bad (more so when touched) as you're always getting minimal capacitive coupling to the environment which is at or near ground potential. My JBL 104s in the office are like that (speakers with built-in SMPS complete with the requisite mains filtering, not earthed) - no hum at all when plugged in, but unplug them and touch the plug (or have it touch the grounded PC case) and all hell breaks loose, even at a modest volume setting. At least it means that the unbalanced input is actually usable.
The DSP computer is an i5 4690k with MSI Z97M-G43 motherboard, single SSD, etc. I don't know the actual wattage it is using because I don't have a meter for that.
A basic Kill-A-Watt is like 30 bucks. This stuff is not easy when you're flying blind. Package Power indicated by monitoring software is a good guide but not the complete picture.
On the software side, you can check processor C-states and clocks e.g. in ThrottleStop, HWMonitor (Windows) or via powertop (Linux). Package C7 should be reached on a regular basis.
I've had a look through the board manual, and going by that (there may have been changes to settings with BIOS updates) I would check the following options in the OC section:
CPU setting - all on default
DRAM setting - all on default (check whether XMP interferes with CPU C-states, disable if needed)
Voltage setting -
CPU Core/Ring/GT Voltage mode: Auto,
Adaptive, or
Adaptive + Offset for undervolting
Other setting -
CPU Features:
Intel C-State:
Enabled or Auto
C1E Support:
Enabled
LakeTiny Feature:
Enabled (I think this is the same as the customary Aggressive SATA LPM setting)
Package C State Limit: Auto or
C7s
Long Duration Power Limit (a.k.a. PL1) and Short Duration Power Limit (a.k.a. PL2) can probably be left on Auto unless a check in ThrottleStop (TPL button) indicates higher than CPU spec values. Those should be 88 W and 110 W, respectively. You may actually want to set lower values here e.g. to accommodate a PicoPSU or cooling solution.
Adjusting Turbo Boost clocks would have to be done within the OS.
I did not see any settings relating to PCIe ASPM. There generally are OS / kernel setings for this (e.g. in the current power plan in Windows), but if you can't get beyond package C3, this may be your culprit. This board doesn't seem to have any extra onboard chips that could screw things up, so that's good at least.
There is an EuP 2013 setting in Power Management Setup that I would test out, but it probably disables Wake on LAN along the way as it's designed to minimize power-off standby power draw. This is handy for all machines that spend a lot of time being turned off and are being turned on manually, and generally saves a watt or so when off.