I am going to install nvidia geforce gt 730 GDDR5. It is a 64 bit video card. But I think I have a 32 bit pciex16 slot(See the image). My question is, can 128 bit and 64 bit video cards fit on 32 bit pci slot?
PCI-express slots are not "64 bit" or "128 bit". They have varying numbers of lanes. The more lanes, the faster the interface, but there is not a "bit width" limitation with fewer lanes.
The longer black slot in your picture appears to be an x16 slot, i.e. 16 lanes, which is the largest in anything like common use. Your GTI 730 DDR5 should work fine in that slot.
The "64 bit" or "128 bit" designation for your video card has to do with its internal architecture (specifically the interface between the GPU and the card's onboard memory), not the slot it plugs into.
PCIe is a serial protocol; the bits come in sequence in a "lane". Even a PCIe x1 slot can support 64-bit addresses. PCIe communication is in the form of "transport packets" that allow for either 32- or 64-bit addresses, and 32-bit data fields. See a much more complete description here: http://xillybus.com/tutorials/pci-express-tlp-pcie-primer-tutorial-guide-1
The two white slots in the OP's picture are of course conventional PCI, which is 32 bits wide.
How did you come to the conclusion that the slot was 32 bit? As far as I know all PCIe slots are x64 by default, that's what gives them one of their advantages over older PCI. There is always the possibility of "just try it" and if the PC doesn't post with the new GPU or it doesn't work in some way you'll know.