The screen assy can be cleaned and reused. Use a new gasket as it might be a crush type design, meaning single use. If the gasket does not seal, air could get into the plumbing and cause the oil pump to lose prime. Torque bolts and nuts to 48 INCH lbs.
Toyota uses their own brand of form in place.
Suggest something like Permatex® Ultra Black® Maximum Oil Resistance RTV Silicone Gasket Maker. Auto parts stores would have and sometimes the auto section of the department stores.
Very important to follow the directions on the tube for curing time. Don't add engine oil (and start engine) until the cure time has passed which may be 24 hours. Otherwise you might have a leak.
Pan bolt and nut torque is 48 INCH lbs. Don't over torque or you can squeeze out all the sealant.
If you don't want to use a gasket sealer on the pan auto parts store seal a normal gasket.
Might change the oil filter.
As to sludge, depends on the extent of the problem. Suggest removing the valve cover an taking a look at the valve train for sludge. The link below has photos of sludge on the valve train.
5SFE sludge - Bing Images
Plus use a flashlight to look up into the crank area for signs of sludge.
Don't confuse sludge with minor varnish built up that is a VERY thin brown coating.
If the engine has a lot of sludge the cleaning process is difficult. Some owners run solvent through the engine. See link below:
Myth or Fact? Gen-4 Sludge problems? - Toyota Nation Forum : Toyota Car and Truck Forums
But before getting to this point check the valve train and crank area for sludge to determine the extent of problem.
Could be just debris on the oil intake.
When fixed suggest changing the oil and filter more often, say 3000 miles. Plus cut open the old filters and look for debris.
Sludge is caused by hot engine oil, water in oil, hot spots on engine metal, failure to change oil sooner enough, poor venting of engine (check PVC system for proper operation and valve and hose are not plugged).