There is no potion of gain strength... do you mean potion of boost strength? Those are intended to be just temporary and act just the way you described. Potion of strength is permanent and only gives 1 or 2 points depending on blessed status. I'm not sure about the walking around strained! part or training with garth though. One thing I know is in the latest prerelease it was changed so training with garth, using herbs and eating corpses won't increase an attribute that's already at it's potential. I'm not sure how long you've played adom but it's much different behavior than 1.1.1 or even the last few prereleases.

I've been playing a dark elven paladin recently and I'm almost finished. I haven't noticed any strange/buggy strength related behavior.

Blessed potions of strength increase strength by 2 points permanently, uncursed potions by 1.
Potions of boost strength give a temporary increase between 5-7 points (roughly) and it returns to normal point by point in a time scope of several dozen turns.
Potions of potential strength as the name implies, increase strength potential but after ~20 strength they are sort of useless.
I've seen very few random strength increases after 20, possibly in the late game where they are irrelevant due to many items granting strength bonuses and guaranteed potions of gain attributes putting stats into their 30ies.

Apparently in the current pre23, it's very difficult to train strength over 15 using "very strained" method.
It used to be possible to do this all the way to 18 before and even 20 with overburdened if you don't mind simultaneous dexterity abuse.
The chance of increasing strength by eating giant/ogre corpses decreases the more strength you have and it's almost impossible to get increases from those after ~20 strength.
Other than that, Garth and his training is still a viable but not very effective method, since it requires serious amounts of gold as training progress and doesn't guarantee increases.

Finally, vampires are powerful undead. They should not be fought in melee if you don't have at least 20 PV and maybe ~30ish DV.
This reduces the number of potentially draining hits and prevents landing hits from doing too much damage.
Outside of CoC graveyard, vampires are mostly treated as out-of-depth monsters, with appropriate rarity.
There's enough near-guaranteed sources of undead slaying, including fireball wands, blessed weapons that deal 1.5x damage to undead and missiles to shoot them.
Typically when I encounter vampires, I can take them in melee but on rare occasions where my PV is insufficient, I will avoid melee at all costs exactly because of strength and toughness drains.

Yes, this was the potion of boost strength, giving temporary boost, and I just didn't noticed.
I'm playing ADOM for a month, so I was just curious and I thought that this must be some kind of a bug, 'cause I've been training other attributes and it wasn't that hard (well, it's really challenging the way it is now).

I've had some random strength increases'decreases too, not sure why was that, but I've could miss some reasons for that.

Thank You guys for comprehensive explanation.

Misunderstanding.