I had this problem also and was driving me insane! I finally found an answer online and hope it works for you.
So all my old notes were in my iPhone folder "On My iPhone" and the new ones were on "iCloud" (which I could see on all my iDevices. I wanted to merge them all into "iCloud" so here's what I did:
Used my old Macbook Pro running Mac OS X Lion 10.7.5 and logged into mail using an IMAP account (AOL) with notes enabled under "Settings>Accounts>AOL>Mailbox Behavior."
On my iPhone, I disabled syncing of notes over iCloud (Settings>iCloud>Notes OFF).
Then went to iTunes (version 11.x) (which was not ever synced with this iPhone since I only sync over the cloud since iCloud became available), the iPhone showed on the left sidebar, went into the sync settings on the INFO tab and turned on SYNC NOTES. It asked me to either Merge or Replace it with the notes on the mac, so I clicked Merge. Then clicked on APPLY and then iTunes synced with iPhone.
Back on Mail, these notes should show up on the left sidebar under "On My Mac." The other folder is called AOL (which had no notes in it). Then I selected all the notes from "On My Mac" and dragged them to the AOL folder.
So Part one is done, all the notes on the iPhone are now on my AOL IMAP's "cloud."
In order to merge the notes from IMAP's cloud to iCloud, I went on my new MacBook Air running Mavericks 10.9.
On Settings>Internet Accounts, I turned on AOL and enabled only "Notes," not mail or contacts (not that it matters I believe).
Opening the Notes app, you will see your iCloud notes (should be enabled also through the above steps and logging into your iCloud account). On the toolbar, click on View and Show Folders List. It should show you both your iCloud notes and the IMAP's notes. Then you select all of the IMAP's notes and drap them into iCloud.
Voilá! All your notes are in iCloud.
Then what I did was turn off AOL IMAP's notes off (since all notes were moved to iCloud).
Back to the iPhone, all my iCloud notes were promptly there. However, there were duplicates from the old folder "On My iPhone" which was renamed "From My Mac." So to get rid of that folder containing all duplicates (the original ones from From My Mac), I synced it again with the old MacBook Pro, but this time I unchecked SYNC NOTES, it asked me to Remove or Not Remove notes from device, I clicked on REMOVE because the folder was empty anyways. Then sync. Back to the iPhone, the folder should hopefully be gone, if not, then manually close the Notes app (double click the home button to show the multitask bar and either press the X or swipe up depending if you're on iOS 6 or 7) and open it again--should be gone!
FINALLY I got rid of this stupid stupid mistake by Apple!!!!
Here are some websites that helped me through this:
http://apple.stackexchange.com/questions/57375/move-iphone-notes-to-icloud/88299 #88299 answer by Motin
and this article
http://www.macobserver.com/tmo/article/Why_apple_strays_from_keep_it_simple
Hope this helps you and many other frustrated users.
Cheers!
PS: On your iPhone make sure you're default Notes account is iCloud in order for all new notes to be stored in the cloud. (Settings>Notes>Default Account)