At the start of this fight, he only has two attacks; the unblockable ice wave that will be rushing towards you and a standard lunging punch combo. The latter can be parried, leaving the Stranger upon for more counterattacks.
Avoid his ice attack and parry/counterattack his punches until his HP drops to 50%. The Stranger will punch Kratos they’ll end up on the rooftop. Keep pummeling him until Kratos gets kicked away in the yard. Press the attack button to pick up the tree trunk and swing it at the Stranger to continue with the sequence.
Press L3+R3 once you see the prompt to enter Spartan Rage mode. After the cutscene, you’ll get a few seconds of unlimited Spartan Rage gauge so use that chance to be aggressive. While in Spartan Rage, you can interrupt the Stranger’s ice wave attack and you’ll be able to close the distance quickly since Kratos will leave towards his target while in rage. After a short while, the Spartan Rage gauge will slowly deplete so you’ll have to finish him off using normal combat. His attack patterns will stay the same so parry his punches and avoid his ice wave until his HP is almost depleted. Kratos will then proceed pummeling him on his own, eventually burying the Stranger under a massive stone pillar.
Walk towards your house and the Stranger will attack once again. After the sequence where Kratos gets thrown to the chasm, climb back up and the third phase of this battle will start. The Stranger will have access to an area-of-effect attack where he jumps and lands on a spot, creating a damaging ice blast. This attack pretty predictable so make sure to double tap the evade button for Kratos to quickly get out of the blast area.
Aside from that, his other attacks is the same. If you’re able to comfortably parry his lunge attacks, you’ll be able to deal more damage since you’ll be able to catch him off guard compared to aggressively chasing after him.
You can also deal more damage by mixing heavy attacks with your basic light attacks, causing his body to bounce helplessly and give you more chances to land your attacks before sending him off flying to a distance.
Keep doing this until his HP is critically low and Kratos will automatically grab him. When prompted, press L3+R3 to finish off the Stranger and end the battle.