Which Is The Correct Plural Spelling? (It's a Trick Question)

Definition: a public vote on a particular issue

Latin has given English a sizable portion of its vocabulary, and one of the reasons that so many of our words are descended from that language is that they have entered our tongue at a number of distinct points. Some, such as butter, date back to the Roman invasion of Britain. Others came to us in the middle ages, from the Norman Conquest. Others still did not arrive until the 19th century, often as part of an expanding scientific vocabulary. Referendum is one of those late arrivals, initially used to describe a vote on the Swiss constitution at that time. Both referendums and referenda are correct.

Of course it will all take time— 
The population must be reassured, 
The boundary must be surveyed, 
There'll be royal commissions, referenda….
—Margaretta D’Arcy and John Arden, The Non-Stop Connolly Show: Part Six, 1978 quote here

Definition: a summary outline of a discourse, treatise, or course of study or of examination requirements

Syllabus comes to English from the Latin sillybus, which actually has nothing to do with buses or silliness (sillybus refers to a label for a book). Both forms of the plural are acceptable, although people might look askance at you if you use syllabi. 

The people who say "syllabi" are probably the same people who use two spaces after a period.

— Sample (@samplereality) August 16, 2015

Definition: a large room used for various indoor sports (such as basketball or boxing) and usually equipped with gymnastic apparatus

Very few people use gymnasia as the plural of gymnasium anymore, but it can come in handy if you want to confuse people. And if you desire still more obscure information about this word, know that it can be traced to a Greek word meaning “to exercise naked” (gymnazein). The naked aspect of this word’s history has been largely set aside in English, although Nathan Bailey, in his 1727 Universal Etymological English Dictionary, defined the word gymnologize as “to dispute naked, or like an Indian Philosopher.”

"Had you rather witness the sports of the gymnasia than the works of artists?" inquired Plato.
—Lydia Maria Francis Child, Philothea, 1836

Definition: a vaporous exhalation formerly believed to cause disease

Most words have a single plural form, while others feel the need to have two. Others are more gluttonous still (such as octopus, the plural of which may be octopi, octopuses, or octopodes), and require three different ways of pluralizing. Miasma is one of those triplets. So if you have more than one of these vaporous exhalations (and we hope you never do), they may be described as miasmas, miasmata, or miasms. 

Not a whit, fair sir—a cordial cup of sack, impregnated with wormwood is the best anti-pestilential draught; and, to speak the truth, the pestilential miasmata are now very rife in the atmosphere.
—Anon., Mary of Scotland, or The Heir of Avenel, 1821

Definition: either end of a transportation line or travel route

Given that the above two words are obscure variant plurals of a somewhat obscure singular form (terminus), it is quite unlikely that you will have need of distinguishing between them. But seeing as how the joy of unexpected knowledge is not regulated by need, we have included them anyway. You may use either terminuses or termini (but not terminusses) with ferocious and joyful impunity.

Home from a world of late-liberal distraction 
To rain and tenfoots clogged with leaves, 
To the life's work of boredom and waiting, 
The bus-station's just-closing teabar, 
The icy, unpromising platforms of regional termini….
—Sean O’Brien, After Laforgue (from HMS Glasshouse), 1991

Definition: an informal record: also, a written reminder

Many usage guides have taken pains to warn their readers of a potential problem with the plural of memorandum. This is not whether or not to use memorandums or memoranda (either is fine), but rather to avoid using memorandas. Some words with similar Latinate endings in English will allow an a ending to take an s (such as agendas), but memorandas is not among them.

But what does our proud Ign'rance Learning call, 
We odly Plato 's Paradox make good, 
Our Knowledge is but mere Remembrance all, 
Remembrance is our Treasure and our Food; 
Nature's fair Table-book our tender Souls 
We scrawl all o'er with old and empty Rules, 
Stale Memorandums of the Schools….
—Jonathan Swift, Ode to the Honorable Sir William Temple, c1689

Definition: one who excels in the technique of an art

Both virtuosos and virtuosi may be found as the plural form of virtuouso, although the former is more common than the latter. Virtuosi is also viewed by a number of usage guides as being overly pedantic, and many will recommend virtuosos instead. So if your desideratum (which is only pluralized as desiderata) is to use the sort of words that usage guides think of as overly pedantic, well, then virtuosi is the word for you.

Those virtuosi who expend their amiable propensities in transfixing butterflies and impaling gnats would here find ample employment from May till November.
—Caroline M. Kirkland, Forest Life, 1850