You should use the select - middleclick action, which on Unix only copies text (and this is cited as a drawback when promoting real copy-paste of rich objects).
What happens (I'm guessing a bit, but I'm fairly sure I'm right) is that OpenOffice recognizes characters in a similar fashion to Markdown (actually, the other way round: OO came first), and formats them.
For example, in OO, if you start typing
"* text" and press Enter, you start an unordered bulleted list. Typing
- text gets you a bulleted list starting with emdash.
1. text starts an ordered list. All automatically.
So what I mean is that this is not an Ubuntu problem, but the Office Suite trying to DWYM. Which, really, seems the best course here. If I copied your question into OO, I'd prefer the formatting to remain, otherwise I'd copy it into e.g. Vim.
Finally, there are some helpful tips here (basically, add a macro that does what you want, assign it to a key combination of your choice). This should work no matter the OS.