Can I find the rationalizable strategies for a game where none of the players has strict dominance but only weak dominance?
In 2-player games, the strategies that survive iterated elimination of strictly dominated strategies are called rationalizable. Note that even if no strategy is strictly dominant, there can be strictly dominated strategies. If you cannot eliminate any strategy, then all strategies are rationalizable.
Only if correlation of players' randomization is allowed, all strategies that are rationalizable (not never-a-best response) are also equivalent to those that survive iterated elimination of strictly dominated strategies in games with more players.
In any case, you can always find rationalizable strategies if a best response exists -- independent of whether a (strictly or weakly) dominant strategy exists.