The Gothic language, the only known East Germanic language, is known to us by a translation of the Bible dating from the 4th century CE, of which some books survive. The translation was apparently done in the Balkans region by people in close contact with Greek Christian culture. The language used is Germanic but has major differences from other known Germanic languages.
In addition, there are numerous short fragments and Runic inscriptions that are known to be or suspected to be Gothic. Some scholars believe that these inscriptions are not at all Gothic (see Braune/Ebbinghaus "Gotische Grammatik" Tübingen 1981)
The Gothic alphabet was probably created by the man who also translated the Bible into the "razda" (language). Some scholars (e.g. Braune) claim that it was derived from the Greek alphabet only, while others maintain that there are some Gothic letters of runic or Latin origin.
There are very few references to the Gothic language in secondary sources after about 800CE, so perhaps it was rarely used by that date. In evaluating medieval texts that mention the Goths, it must be noted that many writers used "Goths" to mean any Germanic people in eastern Europe, many of whom certainly did not use the Gothic language as known from the Gothic Bible. Some writers even refered to Slavic-speaking people as Goths.
There is also the case of the "Crimean Goths". A few fragments of their language dating to the 16th century CE exist today. Assuming those fragments are genuine, it appears to be a different language to the one used in the Gothic Bible (but is still certainly Germanic).