"Prepare for evasive maneuvers!"
If your ship is large enough to have a significant crew compliment that must remain on their feet during combat, that ship is going to have a lot of mass (and hence, a lot of resistance to acceleration). You've tagged this question science-based and physics, so I'm going to assume you don't want to go too far down the rabbit hole of fantastic sci-fi. Thus, without inertial dampeners, it's not just the people that are going to experience large accelerations, it's the ship itself (probably at least in the hundreds of tonnes), so that will put limits on how much force you can apply. Sure, you could add reinforcement to the ship, but that adds mass, which will slow you down, too.
Anyway, the strategy here isn't too different from most sci-fi where someone will shout, "prepare to go hard to port". It's not like the conn needs to prepare to turn the wheel they're already holding in their hand, but it gives everyone else a chance to hang on to something.
Now, at sustained 4g, humans are still going to need some kind of mechanical help to stay in one place. Could you lift four times your body weight for several seconds at a time by hanging on to a safety rail with one hand while you tighten bolts with the other? I can't. There would need to be some safety protocols (and it'd be easy to add some automated audio warnings and interlocks so that if you need to do a 4g turn and your engine officer isn't strapped in, the engine won't fire until she is (or until someone overrides the warning).
Really, 4g is just too much sustained acceleration for humans to do much else than sit/stand strapped in and push buttons.
Magnitude vs. direction
As you know, acceleration is a vector, meaning it has direction. One thing you can do to help your crew is to put your bridge, and possibly other departments like engineering, your med bay, etc., into spherically rotating shells that can self-align themselves with the direction of travel. You mentioned something similar to this for straight-line travel in a comment, but it can be extended to any acceleration if you can design things around spherical pods. At least that way, you can ensure that acceleration is always "back" (or "down", although humans tend to tolerate higher sustained g loads better if they are front-to-back). You'll have to make sure consoles, screens, and supplies all swivel with the crew, but it might help a bit. Departments with large, immovable things that need to be fixed, like the main engines, will be difficult, but those are cases where repairs will probably have to wait until you're done making maneuvers. After all, 4g is a lot of acceleration to expect someone to do physical work with moving parts, bolts flying all over the place, etc.
What about weapons impacts?
If we're talking about sudden impacts from weapons hits that are powerful enough to lurch your entire, massive ship hard enough to throw crew around, but not hard enough to blow massive holes in your hull, I want to tour your shipyards! In seriousness, once your ship leaves drydock, there isn't much you can do about unpredictable impacts but strap in and hope for the best. From a design point of view, you want to deflect as much of the incoming energy as possible, and depending on the weapons used, that could mean lots of sharp angles, or maybe you have some kind of deflector shielding or something. If you have to absorb all of the energy, then all that energy will go into some combination of damage, heat, and acceleration.
In closing, as long as your captains insist on regular safety harness drills so the crew can strap themselves in quickly when the order to turn sharply (or go to battle stations) comes across the intercom, the ship can still make some rather evasive maneuvers while keeping the crew reasonably protected. The rest of my answer goes into some of the finer details.