Aside of using perks, what can I do during the gameplay in order to change my primary statistics?
Several of these enhancements require using a machine within a Brotherhood of Steel bunker in San Francisco. To gain access to this machine without killing anyone, complete 'Get the virtibird plans for the Brotherhood of Steel' quest. (And nab the Advanced Power Armor [+3 strength] and Blue Memory Module [+1 charisma] while you are doing it!) Make sure to give to the plans to the Brotherhood of Steel before the Shi, because the Shi will simply take the plans, where the Brotherhood will give you a copy!
All of these notes are disregarding gains through character creation, and through perks.
Strength +1 via surgery, +3-4 via armor
A strength above 7 is usually unnecessary during character creation. This is primarily because you will eventually find power armor which increases your strength by +3-4 depending on the armor. The suits of power armor are as follows: T-51b Power Armor Advanced Power Armor, and Advanced Power Armor Mk II. You can also make Hardened Power Armor from T-51b Power Armor.
As posted in the other answer, the Red Memory Module can increase your strength by +1 when used within the Brotherhood of Steel bunker in San Francisco with ACE. You can find this chip in the vault within Vault City. It is behind one of the doors which is jammed on the second floor, and if memory serves, you can get to it with a strength of 7 and a crowbar. (use the crowbar on the door)
You can also use Buffout to temporarily increase your strength by two. This can be useful in several situations, like getting to the memory chip in Vault City, or defeating the super mutant in Broken Hills at an arm wrestling challenge.
Jet will temporarily increase strength by +1.
Perception +1 via surgery
The Green Memory Module can be used in the Brotherhood of Steel's San Francisco bunker to increase perception by +1. This chip can be found in the Military Base East of San Francisco and far West of NCR. It is on the third floor (you will need to repair the broken generator on the first floor) in a locker which is easily accessible without encountering any super mutants.
Mentats will temporarily increase your perception by +2.
Jet will temporarily increase perception by +1.
You can only permanently increase this via perks.
You can temporarily increase endurance by +3 using Buffout.
Charisma +1 via surgery, +1 via item
The Blue Memory Module can be used in the Brotherhood of Steel's San Francisco bunker to increase your charisma by +1. You can find this in Navarro, in the underground section, in a locker in the North West corner of the map. If I remember correctly, you need to be told about Navarro's existence before you can go there. Both Matt and Ron will give you a quest to go there.
Mirrored Shades (when carried in an active item slot [the punch or kick slot]) will increase your charisma by +1. You can find these by digging up a grave in Golgotha, or by killing Mason who is a guard on the second floor of the Salvatores bar in New Reno.
You can find Golgotha by either talking to Jules for long enough (you see him when you first enter New Reno), from Myron when you tell him to 'Wait here.' after he has joined your squad (he will offer you a favor, let him tell you about it, you can promptly ditch him afterwords), or by completing the first mission given to you by the Salvatores (where Mason is).
Mentats will temporarily increase your charisma by +1.
Intelligence +1 via surgery, +1 via game story element
The Yellow Memory Module can be used in the Brotherhood of Steel bunker in San Francisco to increase your intelligence by +1. The module can be found in the Sierra Army Depot which can be found by accepting the second quest from Orville Wright; 'Find a way into the Sierra Army Base'. You never have to actually complete this quest, it is just useful to get it so that you know where the base is. You must get this quest before becoming a made man with any other faction in New Reno, otherwise you will never get into the Sierra Army Depot.
The Hubologist zeta scan in San Francisco can increase your intelligence by +1 and luck by +1. But, it can also simply decrease your luck by -1. So you may want to save first. Just let the 'celebrities who are not at all based on actual celebrities' give their speech (North end of the Hubologist compound which is found in the North East corner of San Francisco) and then talk to them about joining.
Mentats will temporarily increase your intelligence by +2.
This can only be permanently increased by perks. Every point of agility gives you 1 action point, so putting this to 10 (9 if you plan on eventually getting the perk) at the beginning of the game is a good way to go because having lots of action points is very useful.
Buffout will temporarily increase agility by +2.
Psycho will temporarily increase agility by +3.
Luck +1-2 via game story elements, +1 via game encounter
The Hubologist zeta scan in NCR can increase your luck by +1 or +2. But, it can also simply decrease your luck by -1. You may want to save before taking it. You can find this Hubologist alone in a building in the center of NCR.
The Hubologist zeta scan in San Francisco can increase your luck by +1 and intelligence by +1. But, it can also simply decrease your luck by -1. So you may want to save first. Just let the 'celebrities who are not at all based on actual celebrities' give their speech (North end of the Hubologist compound which is found in the North East corner of San Francisco) and then talk to them about joining.
Finally, the Pariah dog can increase your luck by +1 if you kill it before it joins your party. This dog can only be found in a random encounter. If you fail a luck roll, he joins your party and you suffer a loss of -1 luck until you kill him. If you manage to kill him.
There is another way to boost your SPECIAL stats legitimately: (though it is basically a free cheat mode)
Upon completing the game (or at least the main quest) and arriving back in San Francisco having destroyed the Enclave Oil Rig, you can travel to New Reno and visit Father Tully. So long as he is conscious (he is often passed out; you can just rest a little and see if he wakes up), you can talk to him and get a little reward: The Fallout 2 Hintbook. "Well, THIS would have been good to have at the beginning of the goddamn game." Using this book will boost all of your stats and skills to their maximum values. And give you a boatload of experience. You can use the book over and over.
Perhaps the best walkthrough for Fallout 2 I have found, which includes all of these details and countless more: https://lemmings19.github.io/fallout-2-walkthrough/
By using ACE in the Brotherhoods of steel bunker in San Francisco it's possible to install memory modules. These give various bonuses, for example the red module increases your strength permanently by 1.
- Red Module: Strength
- Yellow Module: Intelligence
- Blue Module: Charisma
- Green Module: Perception
In the NCR the Hubologists' zeta scan either raises your luck by +2 or lowers it permanently by -1. You need to be a bit lucky here (hah!) as the increase or decrease effect is random. You could semi-cheat by saving before the scan.