Proprietary trading firms pursue a massive variety of strategies. As others have mentioned the only thing that defines a prop trading firm is that they use their own capital to trade. After working inside these firms it is clear that some of them are extremely open to any kind of new strategies as long as they will make money (in the end of the day this is the goal). Sometimes these could be relatively ordinary strategies like market making, but other times it could be strange relative value trades in illiquid products or even spot markets in commodities. I have heard of proprietary trading companies getting into everything from sports betting to cryptocurrencies. Other more generic strategies I have heard of or witnessed in prop:
-Market making in options markets (extremely common)
-Fixed income arbitrage
-Convertible bond arbitrage
-Various kinds of relative value trading (algorithmic or otherwise)
-Discretionary views on underlying
-Volatility arbitrage
-High frequency news event trades