Jectigation

Meaning: Cotgrave tells us this means "wagging or shrugging".

Usefulness: 2 (technically, we should speak of Gallic jectigation rather than the Gallic shrug; shrugging is English, whereas jectigation came to us via French.)

Logofascination: 2 (Etymologically, it's related to pretty much anything that has ject in it, and a number of other words besides.  Although he didn't invent it, Sir Thomas has the first two citations for this in the OED.)

Temulentious

Meaning: tending to be intoxicated, drunk

Usefulness: 1 (an appropriate word for a Saturday: "The city was full of temulentious footy fans." "Friday was temulentious, so Saturday was rather slow.")

Logofascination: 1 (temulent is the base, and also gives us temulence, temulency, temulentive, etc.)

Quadrantids

Meaning: it's a meteor shower which occurs in January, and is named after an obsolete constellation (do constellations get severance pay?), Quadrans Muralis. The Quadrantids now live in the Boötes constellation, but have kept their original name. Boötids certainly doesn't have the same ring to it.

Usefulness: 3 (you wouldn't get to say it much; useful if around astronomers, in need of a particularly difficult trivia question, or looking for a name for an alien species in your latest SF work)

Logofascination: 1 (it just sounds lovely)

Aeromancy

Meaning: Divination by things in the air - generally clouds, but could also be birds, wind, and I guess aeroplanes, nowadays.

Usefulness: 1 (in a town like Melbourne, meteorology is glorified aeromancy. Could also be applied to watching vapour trails in London or any lazy afternoon outdoors: "I'm just off to the park for some aeromancy.")

Logofascination: 3

Ergastularies

Meaning: workhouses, although I like to think that Sir Thomas uses it more as we would 'factory'; it's related to the Latin for a house for slaves or other workers on an estate (ergastula).

Usefulness: 1 (This is what I'm calling my office from now on, and I quite like my job. Also handy to refer to those vast soul-destroying office 'parks')

Logofascination: 1 (all 0 degree words get 1; here Sir Thomas has Anglicised a Latin term - ergastulary, rather than the ergastulum/a/i. This word is referred to so little that it's not even in the OED, something I will be suggesting they rectify.)

Flay the fox

Meaning: Cotgrave gives us a definition and the only etymological speculation I can find online:

"Escorcher le regnard.  To spue, cast, vomit; (especially upon excessive drinking;) either because in spuing one makes a noyse like a Fox that barkes; or (as in Escorcher) because the flaying of so unsavorie a beast will make any man spue." (Current French would be écorcher le renard.)

Usefulness: 3 (depending on your lifestyle. It should be noted that flay the fox sounds suspicious even if you don't know its meaning, so the French version could be useful if you need to describe a particularly good or bad weekend in front of the boss.)

Logofascination: 2 (mainly because it's slightly mysterious slang; I'm not quite sure what it is about old terms for bodily functions, but they're popular.  Jonathon Green has written an almost poetic list of synonyms for vomit, and points out that Australians have originated or are the main users of 38% of these terms. Having recently translated the lyrics of Land Down Under for some Americans, I can't comment.)

Staffage

Meaning: people or animals in a painting who are not the subject of the painting, sometimes used as accessories to provide scale or setting.  Apparently in the nineteenth century there were books of them which you could "cut and paste" into your paintings of windswept-moor-with-tumbled-columns.

Usefulness: 1 (Besides being fun to say if you appropriately accent age, staffage provides an arty way to refer to stock photos, and of course the chance to sound impressive in art galleries, ironically or otherwise. It is also quite useful figuratively, particularly with its coincidental resemblance to staff: "In this meeting you only need attend to Mme Smith; the rest are merely staffage." "This pub is packed: shall we go somewhere with less staffage?" "The sheep are, of course, staffage - the real money is in the uranium deposits.")

Logofascination: 1 (It's a pseudo-French art word we stole from the Germans; a manufactured technical word which, etymologically, is probably just 'stuff'.)