Believe it or not, Pearl and The Owl and the Nightingale are both Middle English. Pearl comes from the late 14th century, around the same period as Sir Gawain and the Green Knight and close to Chaucer, and Owl comes from c.1189 – 1216, at which point the kind of literary Old English used in Beowulf was considered archaic (by the writers of the Peterborough Chronicle, who had decided to quit writing in Old English a few decades earlier). The Beowulf manuscript we have comes from c.1000, and it's the kind of pre-conquest English you'll see Anglo-Saxonists talking about.

Owl and Nightingale is in the same category as other "early Middle English" writings like Layamon's Brut chronicle and Ancrene Wisse, which has changed enough that it's evolved significantly from Old English to be classified as something different, but it's still archaic enough that they're not as accessible to modern readers as, say, Chaucer. Learning Old English would probably make these texts easier to read, but most teaching on it is more interested in and relevant to pre-1066 texts.

All that said, U Michigan has a nice and convenient version of the original Owl and Nightingale poem online that you might have seen already: http://quod.lib.umich.edu/c/cme/OwlC Now, the issue with translations is that poetry in any language is extremely dependent on working within the rules of its own language. A lot of translators will translate poems into Modern English and still set them to a simple end-rhyme, trying to preserve the basic 'spirit' of the original, but if you're worried about departing too far from the source material, any translation will necessarily do that the moment it takes the poem out of the original form. That's why Penguin published the Lais of Marie de France in prose English--the originals are in Old French verse, but translating them and keeping them in a column to look like verse wouldn't make much sense.

All that to say, as long as you're looking at a reliable academic translation, don't sweat it when it looks wildly different from what you'd expect. Here's a modern translation of Owl and the Nightingale from U Southampton: http://www.southampton.ac.uk/~wpwt/trans/owl/owltrans.htm You can compare the two and see (roughly) how things line up.

But! If you want to start tackling learning Old English and make a lot of Anglo-Saxonists very happy, the absolute best resource around is A Guide to Old English by Bruce Mitchell and Fred C. Robinson. It's written for self-teaching at a university level, and while that makes it sound a little easier than I found it, it's hard to beat in terms of quality. About half of it is grammar basics, and the other half is a lot of Old English poetry and prose to practice on, complete with a glossary. Even includes some shorter poetry and a thorough pronunciation guide, which might be helpful for any reciting you'd want to do.