ERA is number of earned runs allowed per 9 innings pitched (runs not attributable to errors). ERC is a term coined by Bill James, the father of sabermetrics, which attempts to forecast a pitcher's future ERA from the number of hits, walks and HR's allowed and K's recorded, rather than earned runs per 9 innings. I'll skip the formula, which is Tutorial B.
ERA+ is simply a pitcher's ERA adjusted according to his ballpark and the ERA of his league as a whole (e.g., normalized). ERA+ gives a pitcher credit for pitching well in a hitter's park, performing significantly better than his league average, etc. and dings him for pitching in a pitcher's park or underperforming the league average. ERC+ is basically the same normalization process applied to ERC. That's an oversimplified answer, but it will give you the general idea.