Excellent question. The words "era," "movement" and "period" are plastered all over Art History, but I don't recall ever, in any class, going over what they are supposed to mean in comparison to one another. I can't find any credible references, either, but will do my best.
First, no matter whether era, period or movement is being employed in a situation, they all mean "historic chunk of time." Secondly, art created during any of the three is distinguished by characteristics common to the era/period/movement. Whichever term is being bandied about, these two factors apply.
The proper name of historic classification is "periodization." Periodization seems to be a combination of art and science, and is only entrusted to Serious Professionals. It's mostly science, as far as I can tell, because those in charge of periodizing use as many factual dates as are at their disposal. The art part comes in when the Periodizers have to use words to describe dates. Someone, somewhere, is always going to disagree with somebody else's choice of words, with an end result that, occasionally, we've got more than one term for the same time frame (and harsh - nay, scathing - words flying between historians).
There's probably a strong argument for foregoing all of this English and using the Vulcan Mind Meld in this periodization business. Since that's (sadly) not possible, here are a few rules of thumb about Art History periodization.
Rule of Thumb #1
Periodization is elastic. It is subject to change if and when new data is discovered.
Rule of Thumb #2: Regarding an Era
An era is usually long, as evidenced by the Baroque Era (around 200 years, if you count the Rococo phase). An even better example would be the Upper Late Paleolithic, an era which covered some 20,000 years' worth of art and a bunch of geological changes.
Note: In recent years, "era" has come to be employed with shorter blocks of time ("the Nixon era") - but that hasn't got much to with Art History.
Rule of Thumb #3: Regarding a Period
A period is generally shorter than an era, though they are sometimes used interchangeably. Going by the dictionary, a period should mean "any portion of time." In other words, period is a bit like the catch-all category in periodization. If we haven't exact dates, or the chunk of time in question was not a specific era or movement, hey - "period" will suffice!
It seems to me that period mostly comes up in Art History when (1) some significant ruler was calling the shots in a specific geographic location (this happened a lot in the far East; Japanese history, in particular, is chock-full of periods) or (2) nobody was in charge of anything, as was the case during the Migration Period in the European "Dark Ages."
To confuse things further, however, certain individuals lay claim to having worked through this or that period. Picasso, for example, had himself both a "blue" period and a "rose" period. So, a period may also be singular to an artist - though I feel it would be more considerate of the rest of us (trying our hardest to keep things straight) to refer to such as his or her "phase", "fling", "passing fancy" or "temporary insanity."
Rule of Thumb #4: Regarding a Movement
A movement is less slippery. It means that a group of artists banded together to pursue a certain commonality for "x" amount of time. They had a specific objective in mind when they got together, whether it was a particular artistic style, political mindset, common enemy or what have you.
For example, Impressionism was a movement whose participants wanted to explore new ways of depicting light and color, and new techniques in brushwork. Additionally, they were fed up with official Salon channels and the politicking that went on there. Having their own movement allowed them to (1) support one another in their artistic efforts, (2) hold their own exhibitions and (3) cause discomfort to the Art Establishment.
Movements are relatively short-lived things in Art History. For whatever reason (mission accomplished, boredom, personality clashes, etc.), artists tend to hang together for months or years and then drift apart. (I think this has much to do with the solitary nature of being an artist, but that's just my opinion.) Additionally, movements don't seem to happen as frequently in contemporary times as they used to. Be that as it may, as one traverses Art History one sees a fair amount of movements, so it's good to know what it meant, at least.
In sum, just know that era, period and movement all stand for "certain amounts of elapsed time, within which artistic characteristics were shared." This is the most important point. People like me (and, possibly, you) lack the credentials to be in charge of assigning these terms, and so may be more happy taking others' words for things. After all, Art History isn't Rocket Science, and life is full of other, more important stress factors.