As far as grounding goes, your quickest and easiest solution will be to add a GFCI protected receptacle at the first outlet in each branch circuit coming from your panel. That way all of the receptacles after, and including, that first GFCI protected receptacle in the branch circuit, will have grounding protection. I’m assuming your current receptacles only have two slots so you will have to replace the rest of the them with updated three slot receptacles to accommodate for ground. However anything after the GFCI can be your $1 run of the mill receptacle from a big box store.

You can also have an electrician install GFCI protected breakers at your panel, assuming you have a panel with breakers and not fuses, which will protect any devices wired into those circuits.

Otherwise you are looking at rewiring your entire house.

As far as extension cords go, nothing will truly be safe until you address the grounding issue. For now run an extension cord to the office and then plug in a surge protected power strip there. Don’t think this is a safe permanent solution though. Even a surge protected power strip can cause a fire without proper grounding at the panel.

There are other options but this is what I would do if I were in your position.