Q: Can I boost my wireless signal with an external antennae, & if so, how?

Have you tried different locations for the wifi router and airport express stations?  Location can have a major effect on signal attenuation in a house.  What is between your office and the nearest wifi node?  It is just wood or wall board or is there a large applicance directly between (fridge, stove, furnace, large duct work, large metal pipes like vent stacks or such)?

You could also try altering the wifi channel - say try channel 1 if using 10 or vice versa (the channels overlap, so pick one as far removed from your current one as possible and try it).

In a 3 story house, ideally I'd want to put the Airport Extreme in the middle floor and as close to the middle of the house as possible, away from large metal barriers like appliances and either on the ceiling or up high at least.  Then put one of the express stations in bridge mode on each other floor (if you need wifi on all floors), but the placement of those may be whatever is necessary to get the coverage to where you want it or need it.

It can take a lot of trial and error sometimes to get things ideally situated in a problematic structure.

P.S. make sure the Airport's are not near any other emmitter either - for example, I use an AT&T 3G microcell at home (basically a mini, low power cell tower in my home) but that needs to be at least 5-6ft removed from my Linksys wifi router or it clearly starts causing some interference issues.  So things like wireless speakers and wireless phones (especially 2.4Ghz phones if using 2.4Ghz bandwidth on a wifi router) can really mess with the wifi signal.

If you have the AirPort Express devices configured to "extend a wireless network" have you verified that they are in fact "extending"' the signal?

If you have a Mac laptop handy, there is an easy way to test. Post back for more details.

You can only extend the signal in one direction using one Airport device.

You can use another Airport device to extend the signal in another direction however...

See this Apple doc:

http://support.apple.com/kb/HT4259

Set up: Components of an extended network

➊  Primary Wi-Fi base station (this is the base station connected directly to the Internet)
➋  Extended base station

Configuring a wireless extended network

To create a wireless extended network, you must place any extended Wi-Fi base stations within range of the primary Wi-Fi base station.

Start with the device that will be configured as the primary Wi-Fi base station.  Then configure your extended Wi-Fi base stations, ensuring that each is within direct range of the primary Wi-Fi base station.The physical location of extended Wi-Fi base stations will vary according to the building environment and may require some experimentation.

THIS WILL NOT WORK PROPERLY...........

Important Note

If another extended Wi-Fi base station ➋ is placed between the primary Wi-Fi base station ➊ and the extended Wi-Fi base station ➌, the extended Wi-Fi base station ➌ will not allow clients to join it. All extended Wi-Fi base stations must be in direct range of the primary Wi-Fi base station

Unfortuantely the last diagram will not work...

You can only extend the signal once, not twice in the same direction...

Hopefully you can get a signal with the one Airport Express and extend that signal far enough for you...

Can I now use my second airport express from another location to extend the signal from the airport extreme?

Yes, if the Express can receive a good signal from the Extreme.

You can have multiple AirPort Express devices on a network, but each one will connect directly to the AirPort Extreme.

Think of the "extend" feature like the hub and spokes of a wheel. The AirPort Extreme is the "hub". AirPort Express devices reside at the ends of "spokes". You can have up to 4 or 5 Express devices if you want.

Each Express communicates directly to the AirPort Extreme, not to another Express at the end of another "spoke".

Just make sure they are not close to being inline like the drawing I showed you above...

Main Base Station -------> Extended ----------> Extender 

(will not work even if it is vertical through the 1st floor to the second floor, etc...)

Like Bob says, spokes of a wheel.

I like to think of 4 spokes in that wheel like a plus sign +

You can extend to the right of the main base station, to the left, to the top, and to the bottom.... But only once in one direction.... wirelessly..

The Maximun number of Express units is up to six according to the Apple Airport Express FAQ section and that depends on the conditions listed below.

Answer: Yes. You can send an AirTunes stream to multiple remote AirPort Express units . The maximum number of remote AirPort Express units is up to six. The actual number that will work in your environment  will depend on conditions such as building composition and radio interference, distance to the remote AirPort Express units, and available network capacity relative to your other usage.