Expressing a date and time is a matter of style, whether dictated by a style guide or simply your personal style. There are thus scores of acceptable ways to phrase your meeting request, mixing words and numerals, abbreviations, formatting of the time, and so on. Indeed, there are dozens of permutations possible just on the time alone— adding padding zeroes, dropping zeroes on the hours, or whether to write a.m./p.m. in small-caps, uppercase, lowercase, with and without periods, and with and without a preceding space.

There are some regional or cultural considerations. As you note, 24-hour time is wholly absent in American usage (known as military time, and used only in a handful of industries). But on the whole, I would say communication between colleagues favors brevity and accuracy over formality. Thus, when e-mailing a co-worker, I might simply ask

Are you available at 2 on the 28th?

If there is any ambiguity as to which 2 or which 24th I intend, I would need to indicate additional details:

Are you available to meet at 2pm Mountain on Wednesday the 28th?

Are you available to meet on Wednesday, May 28 at 2 p.m. PDT?

I rarely, if ever, use o'clock or fractional hours in business writing, as it is both quicker to write and more quickly comprehended with numerals: 7:00 am, 7:30 pm. But it is also the case that Americans always reference direction to the hour, whether in speech or writing: quarter till 5, half past 10, 20 after 8, 10 of 6— too cumbersome for me to write. In British English, where one can say half seven and be understood, that usage might be more common.

Across style guides, years, days of the month, hours, and minutes are almost never spelled out.

The service will launch on Sunday, August 31, 2014 at 6:00 p.m. Denver time.

They are meeting with the vendor on the 4th of March at 12 noon.

We cordially invite you to celebrate the 10th anniversary of Joe's Restaurant on Monday, the 12th of May at 4 o'clock p.m.

Now, you can choose a longer form in order to draw attention to that component, to highlight something unusual or remarkable about it. For example,

She has been working since 5 in the morning

highlights how early she began working, or how long she has been working, whereas

She has been working since 5:00 a.m.

is more strictly factual.

The entire date and time is spelled out only in extremely formal and/or traditional communications:

As a mark of respect for the memory of Neil Armstrong, I hereby order, by the authority vested in me by the Constitution and the laws of the United States of America, that on the day of his interment, the flag of the United States shall be flown at half-staff…. In witness whereof, I have hereunto set my hand this twenty-seventh day of August, in the year of our Lord two thousand twelve, and of the Independence of the United States of America the two hundred and thirty-seventh.

Dr. and Mrs. Jonathan A. Doe request the pleasure of your company at the marriage of their daughter Jane Alice to Lieutenant Commander Frederick John Bloggs, son of The Honourable Mary Q. and Mr. Joseph Bloggs, Saturday, the fourteenth of June, two thousand fourteen at half after eleven in the morning, Anytown Country Club, Anytown.