Is it possible to use the Valyrian Steel Blade to add +1 strength on my unit which is supporting other player during his battle?
On p. 20 it states:
If either the attacker or the defender holds the Valyrian Steel Blade token, that player now has the option of using its ability to provide +1 to his total Combat Strength. If used, flip the token to its faded side, as a reminder that it cannot be used again this round.
So, no, a supporting player is neither the attacker or defender and so cannot use the Valyrian Steel Blade in that combat.