Why does The Force Awakens not use the Episode notation?

As noted in that SFF question, previously the movies didn't either and they were added in later.

However,

The opening crawl for The Force Awakens has "Episode VII" just above the main title to denote that it is, in fact, Episode VII, and thus canon to the other "Episode" movies in the Star Wars franchise.

From my quick bit of research, it would seem the choice was mainly stylistic because the original trilogy films didn't use the "Episode" and number in any advertising. That apparently didn't happen until the prequels came along, and it's believed it was to help audiences to clearly know these films came before the original trilogy.

As such, Abrams is likely just making a stylistic choice to tie the advertising and the films themselves closer to the original trilogy.

First, as MattD already noted, original movies did not include "Episode" part in their titles either. Here are original posters for Empire Strikes Back and Return of the Jedi. I am ignoring A New Hope because it was called A New Hope only after it was clear that it is financial success and there are going to be next movies. It seems that adding "Episode" part to official title is something that prequels invented.

Second, new movie does include "Episode VII" in opening crawl. These are the first words you see when movie begins, right after "Star Wars". So it's not like they are hiding the fact or anything.

Third, money. By putting any indication that your movie is a sequel in marketing materials, studio takes risks that part of audience that is not familiar with previous installments of series will be scared off. And when you have just shelled out $4 billions for rights to intellectual property, taking risks is one of last things you want to do.

People are confused about sequels and they don't know if they have to see previous movies in order to understand what is happening on the screen and enjoy the movie. We had our share of questions regarding previous Star Wars movies here on SE network: "Is it necessary to watch Star Wars: Episode III - Revenge of the Sith before embarking on Star Wars: Episode VII - The Force Awakens?", "What is the optimum list of previous Star Wars movies that I should watch before December 18" or "Should I watch The Force Awakens without having previously watched any Star Wars movies?" are only first few examples.

Probably for this exact reason, it is not uncommon for movie-makers to drop numbers in further installments of franchises. Mission: Impossible did that after three movies (but it seems they want to go back to number in future); Die Hard did that after second movie; Terminator did it in both reboot attempts. Some series, like Pirates of the Caribbean, never put numbers in titles to begin with. Wikipedia maintains lists of movie series having at least two entries - I guess you are free to draw any conclusions from that, but I would say that there are quite a few franchises following that pattern. Putting only a next number seems to be less common practice, but I haven't done a math.

Omitting "Episode <number greater than one>" from title is one of basic risk mitigation strategies. This way movie studio ensures that people who don't know any better will not decide to skip the movie right off the bat. And let us make no mistake - these people are major source of revenue.

It is about the current naming conventions of the franchise.

By 1983, the films were branded as "Star Wars", "The Empire Strikes Back" and "Return of the Jedi". The episode number to the original was added to the opening crawl with the re-release in 1981.

By 2005, with the release of Revenge of the Sith, the films all included their episode names in the titles, with there being "Star Wars Episode I: The Phantom Menace", "Star Wars Episode II: Attack of the Clones", "Star Wars Episode III: Revenge of the Sith", "Star Wars Episode IV: A New Hope", "Star Wars Episode V: The Empire Strikes Back" and "Star Wars Episode VI: Return of the Jedi".

While The Force Awakens is the first film to be released initially with the official naming convention of "Star Wars: Title", all the previous installments are being re-released and branded with the same conventions. The first re-release that follows this naming convention was the steelbook that came out earlier this year.