There are two cards incomming that are reffering to highest or lowest STR.

Roseroad patrol

'... While you control a character whith the highest STR in play, Roseroad patrol gains stealth'

House Florent Knight

Forced Reaction: After House Florent Knight enters play, choose character with the lowest STR in play and discard it from play.

What happens if there is a tie for this specific condition i.e. There are two or more characters with highest/lowest STR?

I don't have a rules quote to back me up, but just judging from the grammar, it appears to allow for ties. Roseroad patrol - "While you control a character with..." It does not say the character, but "a." So as long as your character is one of the ones with the highest strength, Roseroad Patrol has stealth.

House Florent Knight is similar, in that it says to "Choose character with..." If there's a choice, it sounds like it's allowing for more than one. So pick one of the characters with the lowest strength.

Again, I don't have a rules quote on this one, so I'm open to correction, but the grammar of the cards looks clear enough to me.

It's not something that is in the rules. It's based on the text of the card.

As agarrett says, since the text of the card refers to " a character with..." instead of " the character with...," ties are allowed.