IN BATTLE
Valgarv, in battle, is extremely reckless. When he gets serious about something, he doesn't care about his surroundings at all. He just wants to get his job done and if that means totaling the landscape, it's fine with him. He's also very cocky when he fights, throwing insults and acting rather arrogant. Although, his arrogance isn't necessarily misplaced -- he is a very powerful being.
However, his tendency to throw himself into battle can make him very dangerous even to himself. In a rage of fury, Valgarv attempted to transform into an ancient ryuzoku without really thinking of the consequences and was forced to endure very severe pain for his thoughtless actions.
Valgarv also doesn't waste time playing with his prey either. While someone like Xelloss takes the time to torture his opponents and play with them, Valgarv wants to get his job done as fast as possible. He doesn't see why he has to waste his time on someone that can be destroyed immediately. He really enjoys a good battle though, which is perhaps the reason he didn't kill Lina Inverse right away (and also why he was so disappointed that she wasn't as strong as he believed her to be).
POWERS
Valgarv is extremely powerful and is able to use both the power of a high level mazoku (parallel to Xelloss even) and the power of an ancient ryuzoku (just one has the strength of 100 golden ryuzoku). While there are many disadvantages to being a half-breed, there are a few benefits... one being able to harness the immense power of both races.
As a mazoku, he has all of the abilities that Xelloss does. He is able to teleport instantly to any location, is invulnerable to physical attacks (not even the Gornova can damage him) and is able to generate his own power to be used in attacks (blasts of energy, for example). As a ryuzoku, he is able to transform into his dragon form (although not without severe pain) and use powers that ryuzoku can use. Generally, his mazoku-related attacks are generally red in colour while his ryuzoku-related ones are green.
It's unclear but Valgarv claims to have taken Gaav's power for his own. Whether he means he has taken Gaav's place in the world or if he actually has gained additional power after Gaav was destroyed is never explained.
RAVDOMEZEHIS
Ravdomezehis the Spear is one of the five weapons forged by Dark Star himself, and sent to the Slayers universe. Armace came from Dark Star's world to search for these five weapons so that he may destroy Dark Star. At the beginning of Slayers TRY, Ravdomezehis is the most powerful weapon in Armace's possession (Gornova and Galveria were still unfound at the time). Valgarv took Ravdomezehis into his own hands to fight Lina-tachi and later stole it permanently from Armace after Valgarv was betrayed by him.
Ravdomezehis is so powerful that it takes quite a great effort to control the blade of light coming from each end. Valgarv is powerful enough to use this weapon without any effort but someone as weak as Glavos isn't able to. Valgarv uses Ravdomezehis in battle a number of times and he eventually uses it along with Gornova to summon Dark Star into the Slayers world. Using the spear of light for this purpose was probably on Valgarv's hidden agenda when he stole it.
It must also be noted that, while mazoku prefer not to use outside weapons to fight (doing so would only force them to admit that they are not capable of fighting on their own and therefore would damage themselves), Valgarv is not a pure mazoku so using Ravdomezehis doesn't damage him as much as it would for someone like Xelloss.