Visual Kei is a distinctive trend and its usually related to Japanese rock band. Visual bands usually have a strong focus on image by wearing stuff like; lots of makeup, unusual costumes, cross dressers, unique hairdo.
The Visual Kei trend is kinda started by X-Japan where they had unique hair do and cool kinds of clothing in the 1980's..then in 1990's visual kei was being popularized by bands such as Dir en grey and Malice Mizer although Malice Mizer was more closely to gothic instyead
Western observers sometimes confuse visual kei bands such as malice mizer with Goth bands because of the similar makeup and clothing, but most Japanese goths do not consider visual kei to be gothic, and there is very little cultural crossover between Japanese visual kei fans and Japanese goths beyond the outer fringes of the "Gothic Lolita" fashion, which was influenced by elements of gothic style.
People often heard some phrase called angura kei. Angura kei or "Underground" kei is one of the parts of visual kei style, but band with angura kei style doesnt wear gothic costume but they are usually identical with thick white make up, kimonos and stuff that is related to ancient Japan.
And about eroguro kei, it was a forer name of angura kei, but there are several different things actually. Eroguro is all about shocking horror and bizarre sexual imagery with dark humorous overtones. first Mucc and merry are also eroguro kei band, but most of them slowly turned into angura kei which more into Japanese style.