How can I make a sign with a rightclick action displaying a tellraw? [duplicate]

It all has to deal with the escaping of special characters. I am guessing that you used a tellraw generator and then stuffed that into a command sign generator of some sort. They do well but are not very good at escaping characters when it gets complicated. The above linked sign generator even includes:

Note: The sign generator is somewhat fragile. If something does not work try adding a preceding \ to your special chars.

In your case, the command inside the other command requires double escaping of special characters. The tellraw list is what needs the extra escaping.

Quotation marks are escaped \". Then they need both characters escaped for the second escaping. You are escaping the \ with another and escaping the " with \ which gives you \\\". Some call this triple escaped.

In the case of line breaks \n, you need to double escape the \ . The first escape gives \\ and then escape those two for the second escape which gives \\\\n.

One last one. The most complicated of the bunch. The quotation marks in your tellraw text to give you "World of lights" displayed in chat with quotation marks. Truly triple escaped. They are escaped once because they are in the text to be displayed which gives us \". They then still have to be escaped twice just like the above stuff. They are escaped a second time which gives us \\\". Finally, all characters have to be escaped that third time. There are four characters to escape so that gives us \\\\\\\"

You also had some slashes that were not needed in this portion: tellraw @p [\\{

Here is your command with proper escaping of special characters:

/blockdata ~ ~1 ~ {Text1:"{\"text\":\"Right Click\",\"color\":\"blue\",\"bold\":true,\"underlined\":true,\"clickEvent\":{\"action\":\"run_command\",\"value\":\"tellraw @p [{\\\"text\\\":\\\"Welcome to \\\",\\\"color\\\":\\\"gold\\\"},{\\\"text\\\":\\\"World of Lights\\\",\\\"bold\\\":true,\\\"italic\\\":true,\\\"color\\\":\\\"green\\\"},{\\\"text\\\":\\\" \\\",\\\"bold\\\":true,\\\"color\\\":\\\"gold\\\"},{\\\"text\\\":\\\"by \\\",\\\"color\\\":\\\"gold\\\"},{\\\"text\\\":\\\"jackmaster110\\\",\\\"underlined\\\":true,\\\"color\\\":\\\"yellow\\\"},{\\\"text\\\":\\\"!\\\",\\\"underlined\\\":true,\\\"color\\\":\\\"gold\\\"},{\\\"text\\\":\\\"\\\\n\\\"},{\\\"text\\\":\\\"Info:\\\\nTo play you must click the \\\\\\\"play\\\\\\\" sign behind you. Then you will be dropped into the map.\\\\nThis is a map where you must get through the \\\\\\\"World of Lights.\\\\\\\" There will be challenges such as parkour,puzzles,and some other kinds of awesomeness.\\\\nIf you enjoy the map please check out the other maps and minigames available on the server.\\\",\\\"color\\\":\\\"gold\\\"},{\\\"text\\\":\\\"\\\\n\\\"},{\\\"text\\\":\\\"Have fun!!!!\\\",\\\"color\\\":\\\"gold\\\"}]\"}}",Text2:"{\"text\":\"asdasdfasdgdasfeasdf\",\"color\":\"green\",\"underlined\":true,\"strikethrough\":true,\"obfuscated\":true}",Text3:"{\"text\":\"asdasdfasdgdasfeasdf\",\"color\":\"green\",\"underlined\":true,\"strikethrough\":true,\"obfuscated\":true}",Text4:"{\"text\":\"For Info\",\"color\":\"blue\",\"bold\":true,\"underlined\":true}"}

Which gives us:

My head hurts. Tough question.