Oxford and HE are alright, but I have gone games without building them, ever, and won on immortal (in fact not building oxford is fast becoming normal as games aren't lasting that long)
My 2 most important wonders are:
NE: Early NE does so much for the tech capabilities of your civilization it is not even funny. With a decent bulbing plan I have gotten Steel in 600 A.D. and fielded a large army of cannons + macemen in 700 A.D(was so fast I didn't have enough cats to upgrade), Can you say game breaking? If you wanna get an advantage fast, and pursue it, NE is the way to go. Even if you aren't bulbing, you will be settling and probably scientists. The faster you get your GP out the faster you supercharge your civ. Great people are not to be underestimated. An super science city with an academy and 4 GSes c. 800 A.D. is a lovely thing, producing 36 beakers 4 hammers from GP alone without any additional modifiers (54 beakers with rep), once again this can be game breaking Renaissance-Industrial era, which is where I find a settled specialist strategy tends to pay off.
Any way you cut it, the NE does so much for your civ
Other national wonder that can really be game breaking is globe theater.
It is really easy to get a city that can draft 1 unit/turn, and I mean REALLY easy. 1 unit per turn adds up ridiculously fast, especially on epic/marathon speed and this allows for the fast accumulation of armies so fast it feels exploitish.
If you wanna get even more exploity, put GT + HE in same city (some city with a lot of forests + 1 or 2 good food resources) and you will be able to do some seriously abusive whipping as well, HE doubles hammers that are whipped into military units as well so with a combination of drafting rifles + whipping cannons every few turns you can turn out large stacks in very little time.
All things considered however, nothing does as much for a civ as the National Epic. The faster you get your GP out, the better off you are with any strategy other than golden age spamming or corporations, both of which are best suited to late industrial - modern age, and my games rarely, if ever last that long, and if they do, they have long been decided and I am just being lazy and going for UN or something
If you need tech late game, then Oxford is great, but the key to my success on higher difficulties has been opportunistic warfare, which usually involves having a military edge renaissance era or era and because I so often press as soon as I know I can be successful, Oxford is quite often a moot point.