Trying to understand the nuances between ox, steer and bullock

Generally the dictionaries give two meanings of ox, one is the one I paraphrase below:

A bovine (especially a domesticated one)
Merriam Webster
American Heritage Dictionary
Collins Dictionary
Oxford Living Dictionaries

A second meaning, directly quoted:

2.A castrated male bovine
Merriam-Webster Dictionary

1.An adult castrated bull of the genus Bos, especially B. taurus, used chiefly as a draft animal.
American Heritage Dictionary

1.1A castrated bull used as a draught animal.
Oxford Living Dictionaries

The last three definitions specifically mention "castrated", meaning an emasculated male. However Cambridge Dictionary online has two definitions, one listed under English, and one listed under American English:

English:
a bull (= male cow) that has had its reproductive organs removed, used in the past for pulling heavy things on farms, or, more generally, any adult of the cattle family

American English:
an adult animal of the cattle family, esp. a male that has had its sexual organs removed.
(here "castrated" is qualified with "especially")

Further, Wikipedia describes an ox as:

An ox (plural oxen), also known as a bullock in Australia and India, is a bovine trained as a draft animal or riding animal. Oxen are commonly castrated adult male cattle; castration makes the animals more docile.[citation needed] Cows (adult females) or bulls (intact males) may also be used in some areas.
Wikipedia article on ox

So can I safely assume, given all these meanings, that an ox means:
1. Usually a castrated male, but doesn't necessarily have to be.
2. Can also be a female bovine.
3. Is very rarely used for non-domesticated bovines.

With regard to steer and bullock, "steer" seems to be pretty clear; all the dictionaries I've seen simply define a steer as a castrated bull, sometimes using the word "bullock". However a bullock, in addition to being defined as a steer, is also defined in AmE dictionaries as simply a young bull.
see American Heritage Dictionary
Random House Kernerman Webster's College Dictionary
Merriam Webster

Collins, which is BrE, does list "bullock" as "a bull calf" but labels it as archaic.

Finally, there's the Wikipedia disambiguation page which is rather helpful, but actually raises another question:

Bullock may refer to:
Bullock (in British English), a castrated male bovine animal of any age
Bullock (in North America), a young bull (an uncastrated male bovine animal)
Bullock (in Australia, India and New Zealand), an ox, an adult male bovine used for draught (usually but not always castrated)
Bullock Wikipedia page

Here it says a bullock in North America is a young bull, an uncastrated one, whereas the American dictionaries include the definition of a castrated one.

So my question with regard to "bullock" is, in America when the word bullock is used do we not exactly know whether it's castrated or young or old?

You are correct in that steer simply means a castrated male bovine. You don't refer to a lot of feeder steers headed for market as oxen because oxen are draft animals. Steers are more docile than bulls due to the lack of testosterone production in the testes so more apt to be used as oxen/draft animals. Because females (cows) tend to have less muscle mass and are desired for creating more animals and/or milk depending on the breed, they are not usually used as draft animals but can be used as oxen if necessary. In the Animal Science field, we typically only use 4 words to describe cattle: bull, steer, heifer, and cow. For young cattle, we may use bull calf or heifer calf to indicate the sex of the calf. A bull would be an intact male and a steer would be a castrated male. A heifer is a female that has not calved while a cow has had at least one calf. As for bullock, the only people I have heard use that word speak British English as opposed to American English and used it in place of steer.

So in summary, to refer to an animal as an ox, it must be a draft animal and is, more often than not, a steer. A steer is any castrated male bovine. The term bullock is not commonly used in American English but can be used interchangeably with steer.