EBC is a measure of the color of malt and beer and is short for European Brewery Convention (an organization of major breweries in Europe). The following table shows how the colors can be described from pale to black.
IBU is an attempt to objectify the bitterness of the beer by attaching a number to it. The number of IBU in a beer is generally determined using a calculation program. Using various data such as the boiling time of the wort, the hops used and the density of the brew, a value is attached. The actual content can sometimes be lower than stated on the label, even when this is done by laboratories.
More importantly, there are also other factors that help determine bitterness, such as spices and other possible ingredients. So, in practice, you will always have to taste a beer, and besides, tasting is subjective. That said, here's an indicative breakdown: