Launch Automator, and create a new Service. Set "Service receives selected" to TEXT in "any application". Drag the Run Applescript action into the main part of the window. Paste this code in that window:
on run {input}
tell application "Evernote" to activate
synchronize
repeat with selectedText in input
tell application "Evernote"
if (not (notebook named "Stickies" exists)) then
make notebook with properties {name:"Stickies"}
end if
try
create note with text selectedText notebook "Stickies"
synchronize
end try
end tell
end repeat
end run
Now, when you highlight text in any app (including Stickies), right-click and select Services > Send Selected no Evernote, it will copy the plain text into a new note (with a title of "Untitled Note") in the Stickies notebook in Evernote.
The nice thing about this Automator service/action is that it will work with plain-text in any application.

