Calculating Field strength of a air core solenoid
I don't know how to relate oersted to ampere-turns




Or, muliply the oersted value by 1000 and divide by 4\$\pi\$ to get amps per metre (aka ampere-turns per metre). 


  Any clues would be of great help


To get 3000 oersted requires a lot of turns and a lot of amps but I think you should be armed with the knowledge now.

Here's another hint - the H field is "per metre" and the length of your solenoid is 10mm so the amp-turns you need are 0.01 x 239,000 = 2390 ampere-turns so as a couple of examples, that's either 1 amp and 2390 turns (for every centimetre) or 10 A and 239 turns per cm.

I would also consider that the solenoid length should be three times the length of the material to be magnetized to ensure that the resulting flux density is constant along the length; at the open ends of a solenoid the flux can be significantly reduced compared to the centre.