8 or 8.00

Most people would say 'at eight'. Some would say '8 o'clock'. I would use either if I were writing.

'I wake at eight every morning' is better than either.

The Guardian style guide is flexible:

It depends on context. I would use 8.00 in a timetable, but 'eight' or 'eight o'clock' in a letter or essay.

Either 8 or 8:00 would do fine. Note the standard use of a colon when listing the time. 8:00. Using the single . would normally be used for monetary listings such as $8.00.

I know the colon is standard in ISO time, but in Britain, and I daresay other countries in the BrE zone, a dot or point is pretty common. The Times style guide says to use a point for what they call "continental" (24 hour) time formats: 01.55, 14.00 etc. You see all sorts of variations:
no separator at all: 800, 2359;
a space: 8 00; 23 59;
a leading zero if the hour is less than 10: 08:00, 09:59,
all OK. I think this is more an issue of typography and house style than it is of 'grammar'.

Below, in descending order, my local bus, train and airport time formats:

military time --

"oh eight hundred"

On a naval clock it's eight bells 2 2 2 2 (>ship bell<)

As a court stenographer/reporter, I was taught to transcribe clock time as follows:

Figures with a.m. or p.m., use numerals: 10:15 p.m., 6:00 a.m., 3:00 p.m.

For times between one o’clock and nine o’clock, the times are written out, one o’clock, two o’clock, etc., but 10 o’clock, 11 o’clock and 12 o’clock, if it’s after 10:00.

When expressing time without a.m., p.m. or o’clock, use all figures: 8:00, 3:00, 12:00, 10:00.

For the 24-hour clock, no colons, use 2300 hours, 1310 hours, 0400 hours, provided the word “hours” is spoken. Otherwise, 1310, 0400, etc.

Express times with hours, minutes and seconds, for example, as: 23:10:02.

There is also a consistency rule, but that’s TMI.

Don't you just grit your teeth when someone says eleven hundred hours a.m.? Or, eleven hundred hours o'clock?

Hey, don't be such a stranger.