Some elements of Greek mythology traveled East and found their way into Hindu tradition.

What evidence do we have for this? how ancient is Greek to Hinduism?

Afaik there's no evidence that hindu originated from greek myhology. according to some both had a common ac
cestor which is still a topic of debate. watch bbc history of india.

It is the diseases are the Asuras and the herbals are the Deva and Demi Gods.

There is no evidence that it is from Greek mythology.if u search and read about the Hindu mythology u will get to know that it is the most complicated ever.So why don't u think the other way?

The evidence that Hindu Mythology is based on Greek Mythology is based on few facts as below:
1. Hindu Mythology is as ancient as Greek Mythology
2. Few Gods of Greek Mythology are compared with that of Hindu Mythology.

However,
Hindu Mythology is a vast ocean taken into consideration the following:
1 Aadi Parasakthi
3 Supreme Dieties (Brahma, Vishnu, Maheswara (Siva))
4 Vedas (Wrug, Sama, Yajur, Atharvana Veda)
5 Elements (Pancha Bhoothas)
... and more

The reason for saying so.. also could be that Hindu Mythology is made aware to World after Greek Mythology is known. However, there is no comparision.

Hope I made it clear enough :)