My girlfriend is from Venezuela and we are planning a trip from Europe to Venezuela later this year but the easiest and cheapest flights seem to stop in the U.S. Although I can get a holiday visa and ESTA to enter, what does she do? As it will be 2 connecting flights within the U.S and then on to Caracas.
The easiest way to solve this problem is to avoid US-based airlines. These will stop in the US as that would be their main transit hub.
If you stick with European airlines, you can avoid the US completely.
You did not mention from where in Europe, but as an example from UK you have quite a few options.
No. She will need to get a US visa for any connections in the US.
A handy tool for figuring these sort of things out can be found here: http://www.iatatravelcentre.com/passport-visa-health-travel-document-requirements.htm