Learn English – “Adept at” versus “adept in”

Moreover and furthermore are essentially interchangeable synonyms. They're formal substitutes for additionally, also, as well, in addition to, likewise, and too. Those two words are common in academic prose, partially because writers don't combine sentences well or often enough, partly because they need to use them to keep their sentences short enough to read without causing reader fatigue, and partly because it's the easiest way of adding additional information. I try to eliminate as many instances of moreover and furthermore as possible, but it's sometimes impossible.

In addition, they emphasize the "too-ness" of what comes next: {Moreover/Furthermore}, Judge Jones owns stock in the defendant's company, so he should recuse himself from presiding over this case.

The one you use is pretty much a question of personal taste, but my rule of thumb is to put moreover first and furthermore second if the two appear in the same paragraph on in contiguous paragraphs. Others may have a different "rule", but I think it's strictly personal choice.

I think they're all pretty much interchangeable. As I tried to think of an exception, I wondered if throw would be a bit more appropriate for a wild party, and less appropriate for a less festive occasion. However, I found plenty of instances of "throw an office party" on Google, enough to convince me that throw doesn't necessarily imply "wild and crazy."

One additional verb you could use is "host": We are going to host a party on the 11th.

For what it's worth, here's an Ngram, but there's nothing too remarkable there.