As a general rule, Hebrew employs what is known as the Definite Direct Object Marker (or DDOM), which is the untranslatable את (et). So long as the object of the verb is a direct object and so long as it is definite, it should be preceded by this particle. Should, but isn't always. In poetry, for example, it is frequently omitted. Otherwise, the object is indicated through word order alone.
The example that you gave of yisrael is a tricky one. Proper nouns tend to become ossified, and often hark back to a time when the language actually was inflected for case. The biblical literature suggests an etymology for this word as being "one who fights with God", but that is not necessarily what it originally meant.
The examples that you brought for Arabic may not be ambiguous in Hebrew, since the particle translated to the English "to" would usually comprise a distinct particle in Hebrew as well. Thus, yishma el = "God listens" (consider the name yishmael and its biblical etymology), while "he listens to God" would require a particle before God's name (confusingly, in this instance, the homophonous el).
As @fdb comments, there are some texts (such as Ecclesiastes 7:5) in which the particle is omitted. In such circumstances, correct identification of the subject and object needs be contextual.