Cottrell is a form of Cotterell/Cotterill, English, meaning 'cottager' (someone who lives in a cottage, often one connected to a larger house/estate). As for researching it, here in England it was common in Warwickshire, Worcestershire, Staffordshire, Cheshire, Derbyshire and Berkshire - not an uncommon name really. A UK Genealogy site (just google.co.uk for genealogy and you'll find a slew of them) will help you link up with others researching the surname but you'll have to do the step-by-step record collection in the US to get back to the UK immigrant so you can search the line here.
I'm certainly not the only one who knows things! LOL - Far from it! And I'm off having eye surgery tomorrow so I'll be a bit thin on the ground until they take the patch off ;o) Also Scandinavian isn't my area - I leave it to others who know far, far more than I about it. Satu might be able to help with Norwegian/Scandinavian genealogy maybe? Personally I haven't a clue - my folk only go as exotic as French Walloons ;o)