Phil says:

<em>I'm not sure if they're used in British English. I suspect they are not used,</em>

Quite right - they aren't used in British English. Or rather in British contexts - this is about the conventions within the two education systems rather than language differences. A Brit at Yale would presumably talk about being a being a sophomore, while an American at Oxford would not.

<em> .. but would be easily understood thanks to TV and movies.</em>

Not really. Most people outside the US don't know what they mean.

In the context of a movie set in a US high school, it would be clear what 'senior' meant and reasonably transparent what a 'freshman' might be, but 'sophomore' wouldn't necessarily be understood.

Stand on a London street corner, stop people at random and say "What's a 'sophomore'?" and you would be met with blank stares. Most people wouldn't have a clue, some younger people might say 'I think it's something to do with American students', and only a tiny proportion of people would be able to give you a definition. I'm in the second category - I would have to google it to be sure what it meant.

They are common terms in US English.

Confusingly, they are used both for "high school" and "college" students. When there could be ambiguity, it is necessary to say, specifically, "high school senior" or "college senior."

In the United States, a common pattern of education consists of four years of "high school," grades 9-12, ages about 14-18, followed by four years of "college," ages about 19-22. "High school" is often a public school in your home down. "College" is often the undergraduate program at a university.

So, in high school, grades 9-12 are also called freshman, sophomore, junior, and senior year, and the students in them are called freshmen, sophomores, juniors, and seniors. The proud graduating senior may then go off "to college," where he finds that he is now, once again, a lowly freshman--a "college freshman."

The group of e.g. all seniors in a high school is "the senior class."

Grade numbers are used only in high school. So, a high school commonly has grades 9 through 12. The four years of a typical university undergraduate program are <em>never</em> called "grades 13 through 16."

These terms are definitely very frequent in American English. I'm not sure if they're used in British English; I suspect they are not used, but would be easily understood thanks to TV and movies. These terms are used in both University (US: “college”) and high school (students are between 13 and 19 years old). You could say a “college senior” or a “high school senior”, although it’s usually obvious from the context. Interestingly, the word "sophomore" is a good example of an oxymoron, as it is a combination of Greek roots "sophos" (knowledge, wisdom, as in "sophisticated") and "moron". 

Thanks for clearing that up, Su.Ki. That makes sense about the terms relating to the respective educational systems, rather than differences in language. Kay: Good job using the singular verb in your title question! It would be tempting to use the plural, but since we’re talking about one system for referring to students in different years, it is notionally singular. (We’re not actually talking about the students themselves.)