Custom White Balance is the solution. Shoot a white piece of paper (seamless, typing, foamcore) if you don't have a target. Then it will not matter as long as the Color Temp remains fairly consistent.

You might also want to post a similar question in the Olympus forum. There is more expertise potentially availble there as to any particular issue with Flourescents and White Balance with Oly DSLR's.

Table top photography isn't usually a problem with the 'flicker' just use a long enough exposure to counteract the cycle rate of the lamps. Do let the lighting fixture operate at full power for 10-20 minutes prior to use as the ballasts (or other solid state controls) will even out during that time.

Looks like you are a newcomer to PR, Welcome!