Is huge gaps between wall and baseboard normal after reinstall them?
If the new hardwood floor was about 3/4" thick, there may be no way to nail the baseboard trim to the 2X4 plate. That new height of the finished floor raised the trim above that 2X4 plate. You may need to locate the studs and use them as your nail surface. This is common when you add a second floor on top of another floor. You could also try nailing near the bottom of the trim, on a downward angle to try and "grab some wood" near the bottom of the trim boards. A nail gun may help in this process.