Could there be an exploit by creating millions of meaningless transactions? Would it be possible to hamper the network's efforts in validating blocks by creating millions and millions of bogus transactions- simply sending back and forth say 0.1 BTC from address A --> B --> C --> A and so on endlessly? Obviously this would hard to do by hand but if there were an automated script it could be done theoretically quite easily..

Or would this strategy have absolutely no effect?
You need to provide fees on bitcoin transactions, in which case, you are producing economically valid transactions and will run out of money eventually.

Currently the min fee is 0.0001 (BTC).

Listed here - https://en.bitcoin.it/wiki/Transaction_fees