While there is no way to actually switch a VDI between fixed-size and dynamic, you can clone the existing VDI into a new one with different settings with VBoxManage.
VBoxManage clonehd [old-VDI] [new-VDI] --variant Standard
VBoxManage clonehd [old-VDI] [new-VDI] --variant Fixed
If you want to expand the capacity of a VDI, you can do so with
VBoxManage modifyhd [VDI] --resize [megabytes]
Resizing only works for dynamic VDI images. However, you can combine the resize information with the conversion information to expand fixed-size VDIs. (E.g., convert a fixed-size image to dynamic, expand it, and then convert the dynamic image back to a fixed-size image.)
If you want to compact the image as much a possibly, be sure to zero out the free space. This can be done in Linux by using the dd command to write endless zeros to a file and then deleting that file. (With the caveat of the reserved space of EXT and other file systems.)