What do the:  Get Access Class.Java/Exploit.BytVerify.F trojan ; 
Dummy Class-JS/IE.start trojan  ;  Installer
class-Java/openconnection.F trojan   viruses that I have recently
found on my machine with NOD32 do?  Can I prevent them from getting on
my machine, I thought that was what NOD32 was supposed to do?

BytVerify Trojan is detailed in the following security bullitin:
http://www.microsoft.com/technet/security/bulletin/MS03-011.mspx

IE.start Trojan is detailed below:
A script trojan that alters the default start up page that Internet
Explorer uses by changing
HKEY_CURRENT_USER\Software\Microsoft\Internet Explorer\Main\Start Page
Written in script code and run from an .ASP, .HTM, .HTML, .VBS, .VBE,
or .HTA file.  Normally it changes your homepage to one that would
bring in ad revenue to the trojans maker (mobile ringtone webpage
etc.)

and Openconnection:
A program designed to retrieve and install additional files, when run.
Most will be configured to retrieve from a designated web or FTP site.

NOD32 is an antivirus software, it essentially deals with the
consequence, not the cause.  It will scan any file on your computer,
but it can't prevent the file getting on to your machine (more on this
later).

What you will probably find is that the files you have listed are in
your temporary internet files directory which due to the permission
structure, makes it hard for NOD32 to delete, if you can, manually
delete all the files in your temporary internet files folder (usually
c:\documents and settings\yourUserName\Local Settings\Temporary
Internet Files) you may need to tools > folder options > view, and
check the "Show hidden files and folders" to see the directory and
contents.

To prevent you getting the trojans/viruses again, please use a
different web browser, Firefox (www.getfirefox.com) is free and far
more secure then Internet Explorer, if you don't mind paying for a
browser, Opera (www.opera.com) is also a good choice, and please, pass
the message around! :]

Also install a spyware remover, SpyBot is very popular (and free)
http://spybot.safer-networking.de/en/ and AdAware (www.lavasoft.com)
is also a sound option.  It will work hand in hand with whatever virus
software programs you use, and help to check a wider variety of
problems (a virus scanner is only as good as it's virus database, so
the more the merrier!)

Hopes that helps!