Katelicious, I'm wondering what you mean by "not usable" with regard to TGA files. TGA is the most common 2D format utilized in 3D, and has been for decades. The vast majority of texture work, still renders, image sequencing, etc., is done with TGA. The format is also widely used in other industries, such as video editing, special effects, etc. For any non-web-based on-screen work, TGA is incredibly important. So what did you mean?
What exactly are you trying to do for which you think TGA will be ill-suited? About the only things I can think of would be print or Web work. I think it's safe to assume print is out since you mentioned JPEG and GIF. No one in their right mind would want to print either of those. So that leaves the Web. Are you looking to put your SL images onto a website or something?
Whatever you're doing, I'd caution you strongly against converting your images to GIF. GIF only suppports 256 colors, so it's almost a given that any photographic imagery, including SL screenshots, will look like crap if you make GIF's from them. GIF is best suited for diagramatic or illustrative work, simple animations, simple logos, etc. If you're looking to post screenshots to the Web, go with JPEG or PNG. For visual quality, PNG is the best choice, since it's lossless, but for maximum compatibility, JPEG still has an advantage, since it's a much older format. JPEG can be read by just about anything.
To answer your question about programs, any full-featured image editor, such as Photoshop, GIMP, Paintshop Pro, etc., can convert TGA files to any other format you'd care to use. Photoshop can batch convert a folder full of images in just a couple of clicks.
Other alternatives would be dedicated converters, such as the already mentioned Irfanview.
As for why your converted mages are coming out grainy, I can think of two easy explanations. First would be if you're using GIF, since it's not meant for this kind of work. The TGA images you're pulling from SL have up to a little over 16 million colors in them, while the GIF's you might be converting them to can only have up to 256 colors. That means you can potentially lose more than 99.99% of your existing color information with GIF. So don't go that route. If you've been doing JPEG, then my guess is you've got the quality settings too low. JPEG compression is very lossy, and can look anywhere from OK to absolutely dreadful, depending on how you optimize it. JPEG's can't ever look really good, unless you're dealing with very large imagery, much bigger than anything you'd be pulling from SL.
I haven't used Irfanview in a very long time, so I don't know off hand where to find its JPEG quality options, but a quick Google search for "Irfanview JPEG qualtiy settings" just turned up this article:
http://www.dpnotes.com/the-best-way-to-save-images-as-jpg-jpeg-in-irfanview/ . Looks like worthwhile reading.