You need to paste the text as “HTML format without comments” (Edit > Paste Special > HTML format without comments) and then select everything (or just the images if you prefer) and goto Edit > Links > Breaks Links (the last button on the bottom right of the Edit Links dialog).
NOTE: To select all images in the Edit Dialog, click on the first, scroll down, press the Shift key and then click on the last image name. Click on Break Link to break the links for all images. The list will be empty after the command has been completed.
By default none of the StarOffice descendants (Symphony, OOo, LO or AOO) pastes the images, just the links (which are useless if you are offline), so you need to break the links. Pasting in MS Word does paste the images as expected so this is quite surprising for someone migrating from MS Office.