will grant read permission for that file to everyone who is not the file's owner and is not a member of the file's group (which fits the intended use for user nobody).
The command:
chmod -R o+r /var/log/iptraf
will change the directory named and all files in the file hierarchy below that directory. But, again, log files in an iptraf directory may well show details about users on your system, the sites to which they connect, and data sent to and received from those sites that should be considered PRIVATE data and not made visible to everyone who wants to snoop around on your system.
If the file is removed and recreated by some process on your system you will either need to run this chmod command in or before running this script or you will need to track down the process(es) that create(s) this log file and either change the umask when creating the file or change its mode immediately after creating it to grant read permission to everyone.
Note that a script running as nobody won't have permission to use the above command to change the mode; chmod will succeed only if it is run by the file's owner or by someone with appropriate privileges (i.e., root on systems that don't have extended privileges mechanisms).
I STRONGLY REPEAT MY WARNING THAT WHAT YOU ARE DOING IS LIKELY TO MAKE PRIVATE DATA VISIBLE TO THE WORLD!
To get back to a sane state you need to restore the owner and group of /var/log/iptraf and /var/log/iptraf/tcp_udp_services-eth0.log and then (if you really don't mind being sued for disclosing private data) add search permission for owner, group, and other to /var/log/iptraf. You also NEED to remove write permission for class other from /var/log/iptraf/tcp_udp_services-eth0.log.
Although I can't tell what permissions were originally granted the various classes of users by the designers of your system, it is obvious that you did change the owner, group, and permissions on /var/log/iptraf/tcp_udp_services-eth0.log and /var/log/iptraf. If there are any daemons running on your system not running with "all privileges", it is highly likely that with your current settings, you have completely disabled adding log entries to all files in /var/log/iptraf by those daemons unless they had (and still have) the log file open before you changed permissions on /var/log/iptraf.
OK. Now that you're back to a sane starting point, since ls doesn't show that any extended security controls are in use on these directories, the following should loosen security controls enough to allow everybody to read /var/log/iptraf/tcp_udp_services-eth0.log:
chmod 755 /var/log/iptraf
I will take your word for it that you know how to safely handle security issues. In you first message you said that you didn't know who was running the script that is doesn't have permission to read this log file (so you added a call to whoami to see who it was). The fact that it showed that it was being executed by user-ID nobody means that it was likely started by a request from a remote system. You are changing the system's security features so that anyone on the same network as this server can read any log file in that directory. I'm not familiar with the iptraf application, but IP traffic being logged on a server need not originate on that server. Just because you're the only one who logs on to that server doesn't mean that IP traffic can't contain data from other users, and doesn't mean that users on other systems on your network won't be able to read sensitive information from log files in that directory.