34kWh/day is diabolical. That's 24h of 1.5kW of draw (or, if just counting the waking hours, ~2.1kW of continuous draw), which seems insane; you only have maybe 10kWh accounted for with your additional use.
It's all but guaranteed you have some kind of electrical heating element somewhere in your house; in-floor heating (kitchen/bathroom, if anywhere generally), auxiliary heating through a heat pump, a baseboard heater in a wall in a utility room/crawlspace, etc. Either that or you're charging an electric car. Do you have your thermostat set to heat/cool, or just heat? It should be set to heat right now, to ensure your A/C unit outside is not turning turning on (which would be "bad"). Do you have a hottub? Pool? Heating elements on the roof to melt snow? Any kind of device that heats your garage? Towel heater?
If you can't find auxiliary heating elements normally, I suggest going to your breaker box and looking for anything that is greater than 15A; this might help you find circuits that are designed for heavy use, and thus potentially could account for your odd situation (especially if everything is labelled). Notable circuits that will be greater than 15A, really heavy hitters will be linked together (two breakers side-by-side will move together). Normal "large" circuits would be A/C, stove, dryer (if electric), sub-panel (if present), any breaker for the kitchen. If you see anything labelled "heat", that's a for-sure place to look.
Edit: For reference .... I have a 1,250sq.ft 1970s brick ranch home ... 1 gas stove, 1 electric, gas forced air, all LED lights, 2 plasma TVs, an always-on server/Internet/smart home setup that draws about 100w continuously. On XMas day, I cooked for 37 people; both TVs on all day, all the lights on basically, and both ovens/ranges running for like 7 hours (many oven items: turkey being one, but lots of frozen stuff like lasagnas, meaning even more power use as the oven tries to thaw them), electric warming trays, an auxiliary fridge from like 1970 for drinks was plugged in, and a bunch of other stuff I don't remember I am sure. My normal use is about 9-11kWh, that day was 19kWh. The GF also did her hair at ~1am that morning. There's no way your use accounts for 28kWh.
Edit2: As for one of your devices leeching power like mad: it would have to be drawing an insane amount of power. Imagine it's your laptop: if it was on for like 5 hours, it would need to be drawing 3.6kW to account for your additional usage.