Okay, so there's this word, "tracing," that gets used from time to time on the Internet and in movies, that shows something akin to someone following a path along the lines of a specific person's communication online. In reality, nothing like this happens, or is possible. However, here I will break down the different parts of the trail that a person leaves behind as they access a website, and explain the reality behind all of it.
When you access a website, your computer sends a request to the web server. When that server gets the request, it logs it, along with the IP address from which that request came. Note that I didn't say "the IP address of your computer." It usually is, but if you use a proxy server to connect to the website, the IP address of that proxy server is what will be logged, rather than your IP address. The log entry will contain the above-mentioned IP address, the content of the request itself (the HTTP GET, POST, etc. command that was sent, along with any parameters) and the "referrer", which is the URL of the page that contained the link you followed, if applicable. A separate log entry is created every time your browser makes a request to the web server, and the logs are stored at the server. While it's possible to turn off logging, it's a terrible idea for the webmaster, because those logs are super useful for troubleshooting errors in web applications, detecting certain types of application hacking and reconnaissance, as well as analysis of user activity (like "Are there any parts of the website where a lot of users just bail?") that help them improve the user experience. What can someone from LE do with that? Well, if they want to find out who is behind any specific IP, they need to get a subpoena to go to the ISP that owns that IP, to get the account information that corresponds with the account that was using that IP at the time. They need to do this for each and every such lookup, stating their case to the court. It sounds like a lot of work, but it's actually somewhat cookie-cutter, so it's just a bit of work. Mind you, for a busy site, if they wanted to track down everyone they'd have to do this tens of thousands of times. And they'd need a search warrant, and to seize the web server, in order to get those logs without TER just handing them over (which would be suicide for them as a business).
Potentially, someone could observe the communications between browswer and web server, but this is a huge deal; they would need a warrant to allow wiretapping, essentially. There are two kinds of wiretaps: ones that are only allowed to classify who is talking to who (or, in this case, what is talking to what) without recording or observing the contents of those communications, and the more commonly thought-of kind, which records the actual communications. This would be a lot of work for LE, both from a procedural perspective and from a technical one...they would use this if they had some reason to go after a specific individual, and that person happened to visit TER, rather than as a way of going after TER members.
The other set of evidence resides on your machine. A web browser works by pulling files down and then showing the local copy to the user. Thus, there's a cache of things you download (as you already know since you're clearing that cache), and a history of what you visit. Be aware that deleting these filed doesn't really get rid of them; it's quite simple with forensics to recover 'deleted' files from slack space, since deleting them just removes the pointers in the file system to the data. In other words, if the part of the hard drive that contained a deleted file hasn't been overwritten with something else yet, the file still remains and can be recovered. The solution for this is a program like Eraser, which overwrites slack space with random data, and can be scheduled to run on a daily basis.
Last risk is of a keylogger on your computer, either put there by LE or by a bad guy (who would then blackmail you...don't joke, as at this very moment a trojan horse called Kenzero is doing this sort of thing to people with regard to their porn surfing). If LE has a warrant to break into your home and put such a piece of software onto your system, you're probably pretty screwed, as to get that kind of authority (and put that kind of horsepower behind it) they really have quite a lot of interest in you specifically. This is the kind of investigatory activity reserved for high-level members of organized crime, cases where espionage is suspected, etc. So don't worry about it, unless you're spying for another country, planning an act of terrorism, or party to certain social organizations that take "whacking" to the next level 
Against the backdrop of all of this is the following: what LE would be interested in is a local affair, subject to local jurisdictions. And going after people based on their use of this site would be a massive undertaking that would span a lot of different, disconnected jurisdictions, over events that truly aren't that much of a bother to LE in the first place. They have easier, bigger fish to fry.