This is one of the most common claims thrown around about Jesus by non-Christians of various varieties. Of course, the problem with all these theories is that they are based on zero hard evidence. Most common is the claim that Jesus went to the Indian subcontinent and was influenced by Hindu thought. Any such claim comes either from an unsubstantiated report whose origin is many hundreds of years after the time of Jesus or from people scanning the New Testament and claiming to find ideas from other religions in the sayings of Jesus.
You are asking not the classic question of whether Jesus traveled to other countries, but whether he studied these religions, not necessarily by traveling. We cannot prove that Jesus did not study other religions. In fact, it is only reasonable to assume he was aware at least on some level of the religious movements common in the Eastern Mediterranean in his day. However, even if he did study other religions, it is not clear this would change the meaning of his teachings.
Serious scholars are unanimous as far as I know in their conclusion that Jesus’ religions background is principally that of a Galilean Jew. His thought and his words are saturated in Old Testament, influenced as well by Jewish thought of his time. No serious scholar that I have heard of so far has claimed that Jesus quoted from religious sages outside Judaism. We find no quotes from the Hindu Vedas or Pagan religious thinkers of his day. Besides, there is no extant evidence that Jesus ever traveled outside the Eastern Mediterranean.
So, any claim that Jesus studied other religions is based on sheer speculation–certainly not on any hard evidence.