I experience a serious amount of lag in this game (singleplayer), especially at critical situations as gunfights. How is that even possible for an old game like this? I run it on a 2013-state-of-the-art computer (Win7). Yes, the settings are on the highest - but again, this game is more than a decade old. It should be possible, without lag.
Someone know why, and how to help it?

Did you have v-sync on? I know that some games(old and new) can feel terribly laggy even with high fps, turning on v-sync can smooth things out.

Hmm, I can't find any V-sync under options. Neither in video nor advanced.

Sorry I was thinking there was an option for this in the video settings. You'll have to set it via your GPU software, I'm not sure of the steps for AMD but I do know nVidia.
If you open 'NVIDIA Control Panel', go into 'Manage 3D Settings', then under 'Program Settings' select MOH from the dropdown list. You can now change the v-sync and any other options you like, and be sure to click apply before closing.

^
I've found a lot a stuff like Anti Alialising, CUDA, Shader-cache and such - but V-sync options.
I do however found a option called "Virtual Reality pretreated pictures" (the last two words are in Danish in my system, so these I've translated (with sucky Google Translate, since my dictionary don't have one of the words), and these will probably not appear in the same way in English versions). Is this the same as V-sync?

V-sync should be the option above 'Virtual Reality Pre-Rendered Frames'(thats how the english version calls it). Note that v-sync is titled 'Vertical Sync' so I'd expect it to say 'lodret synkronisering'(Google Translate to Danish).
I've attached an image of what I see when I open nVidia's Control Panel(driver version 350.12), with the v-sync option highlighted.

I'm doing the best I can not to start a rant about the improper use of the word "lag".

MOHAA runs on a modified Quake 3 engine and you often don't want to run it at ridiculously high frame rates. Your modern computer may be rendering the game at 900 frames per second but it often messes up the physics and control input on older game engines. Vertical Synchronization (V-sync for short) forces the video card to render every frame fully rather than just firing them up on screen half finished with the previous frame still showing underneath, which isn't really what you are looking for, but it has a beneficial side effect in that it also limits the frame rate to 60 frames per second.

This is good because in the old days this was considered very high but still possible on the best computers. Only very old games start acting strange when rendered at about 60 fps (like Outcast and Interstate '76). Secondly, it is a lot less stressful to your graphics card and so it won't overheat from working harder than it needs to.

If v-sync does not fix the performance of the game, I think you should try a different renderer if possible. The game should have the option of OpenGL or Direct3d.

Yeah, it's that side effect of reducing the fps that can make a massive difference for some games.
As for trying a different renderer, I'm not to sure we can.

Now I've found it. Thanks!
I've set V-sync to "Yes". The "lag" still appears, however in a bit smaller scale.
For do I reduce the fps? Is that in-game, or in nvidia control panel too?

I'm not sure what else you can do to fix this, but what FPS are you now getting?

I don't know. Do I see that in-game or elsewhere?

You'll need to use additional software for this, 'FRAPS' is the most popular for monitoring FPS.
You can get it from there website, install it and then run it while in game. It will show you current FPS in one for the corners(default top left I think).
http://www.fraps.com/download.php

But what might be more benifical would be 'MSI Afterburner', primeraly used for OCing but it's monitoring tools might help see where the issue is. You can setup its monitoring to show FPS, CPU and/or GPU usage, Temperatures, Memory usage and more.
http://gaming.msi.com/features/afterburner
This is what I use to check my FPS and more while running games. In MOHAA it show 90fps for me, with no v-sync, GPU usage at about 20%. CPU usage was max 80% on core5, all other cores were below 15%.

Hi again

I've tried to run MoH with Fraps running, at it says 60, and that with V-sync on. With V-sync off, it says 90.
So, should I try to increase or decrease fps?

Is it constantly showing this number, even when the game is "lagging" as you phrased it? By the way, lag is not the appropriate term to use here but we might get to that subject later. For now, let's just stick to troubleshooting.

The reason I ask is because if the game is running poorly even though it is rendering 60 frames per second the problem is probably something other than graphics entirely.

@Sufyan:
In situations of small "lags", the number are slightly decreasing to 55, and after a very short time (a quarter of a second) it returns to 60. In situations with heavy "lag", the number decreases to 45, and increase back to 60 within a second.
In this case I play with V-sync on.

Sorry for the wrong use of the term "lag". I am not IT-skilled enough to know a more suitable term for this situation.