I was told over the weekend that while Obama may be eligible according to the constitution, old English common law actually trumps the constitution and according to that he is actually an English citizen
They've got that exactly backward. Common law fills the gaps where the Constitution and enacted laws (both federal and state) don't exist or where gaps exist. When it comes to citizenship, its definition, etc. the Constitution and federal law completely cover the field...there is no real common law applicable to this issue...unlike, say, obscure property rights, etc.
PLEASE understand, the Constitution, Federal and state law ALWAYS trumps common law.
ETA: what is true is that many enacted law -- e.g. in the area of property, torts, contracts, etc. -- reflect common law approaches to an issue or encorporate common law practices, but as said above, enacted law always trumps common law, and the Constitution (and its protections and prohibitions) essentially always trumps enacted law.
I hope your friend isn't trying to make a case for him/herself, say, on taxes and why they aren't paying them, based on some obscure common law doctrine, they'll be going to jaiil.