Some say that there was some relation between zoroastrianism and the ancient vedic religion. Are there any aspects of judaism and hinduism that have any similarities due to this influence?

Not really. So let's explain. Zoroastrianism and Vedic religion are similar because they have the same rough root, that spread into different areas, where they not only developed differently over time, but there was likely different pre-existing groups whose indigenous beliefs were incorporated differently into the ur-Indo-Iranian belief systems.

There are some clear Persian influences on Judaism, but this is only after the Babylonian exile when the Persians allowed the Jewish elite in Babylonia (and others that fled to Egypt) to return to the Land of Israel from their exile, rebuild their Temple, and restore worship. However, most scholars agree that the basic framework for "Temple Judaism" was already set before the Exile (at the latest during the reigns of Josiah and Hezekiah). Even those who argue against this tend to believe that the Temple Judaism framework was set very early after the establishment of the Second Temple, so before there was a heavy Persian influence.

There are some ideas that are often credited to Persians/Zoroastrians. The word Hebrew word pardes, which our word "paradise" comes from, comes from the Persian word meaning "walled garden". In three places in the Hebrew Bible (all in post-exilic parts, obviously), it means a garden or orchard, which eventually it seems got associated with the Garden of Eden, and the idea of the restoration of Eden as the "world to come". So even though the word is Persian, it's hard to connect it to specific Zoroastrian theology and there's certainly no corresponding Vedic idea.

Jewish ideas of satan and angels are ideas often said to show Zoroastrian influence. Satan, meaning literally "adversary", is probably a pre-exilic idea, but the idea certainly developed more after the exile, perhaps with Zoroastrian influence from ideas about evil. There's no strong evidence for this. There's a better case that angels developed under Zoroastrian influence. For example, the first time we get named angels is in Daniel. The popular iconography of angels also owes more to Zoroastrianism than earlier books of the Hebrew Bible. So these angels (and extra canonical demons) have often been taken as indication of Zoroastrian influence, but this is a part of Zoroastrianism that isn't particularly close to any part of Vedic religion I'm familiar with. Even though the Avesta term daeva is clearly etymologically related to the Vedic term deva, they're quite different. By the time Zoroastrianism may have influenced Judaism, it was already quite separate from Vedic religion. This makes sense--the Rig Veda was composed somewhere in the very broad range of 1700–1100 BCE and the oldest Zoroastrian texts we have are from somewhere between maybe 1000--500 BCE (the dating is quite hard, I've been lead to believe). The Rig Veda and Old Avestan texts are the ones that show the most similarity between the two groups, because they're closest to the split between the populations (which occurred maybe before 2000 BCE). As we move forward in history, the two populations diverge further and further. Zoroastrians only encountered the Jews in force after the Babylonian exile (and probably before the Greek take over), so exerted the strongest influence between 538 BCE and 334BCE, when Judea was part of the Achaemenid Empire. That is to say, long, long after proto-Zoroastrian religious traditions split from Vedic ones.