I tested my Strida SD to an uphill ride last April 8 2012. The road was 16kms with half of it going uphill and the SD was able to manage it. It passed the test and the downhill return trip was awesome. The question though is I bought a 2nd hand SD and planning to upgrade to 18" wheels. I think Genuine_S already did with the cool rims. How was the gearing? Was the 2nd gear too hard?
Theoretical is the difference of the gear ratios ~ 11 %.
(Amuro has calculated that for us already here: http://www.stridaforum.com/forum/viewtopic.php?f=2&t=2688&start=0&st=0&sk=t&sd=a).
Practical is the felt difference not that much, because the 18" tyres (1,25" or 1,35") are not as wide as the 16" tyres (1,5") and the 18" tyres are normally used at higher pressure.
The 18" Kojak tyres do not have any profile, which is also reducing the roll resistance (disadvantage: less comfortable due high pressure).
For my feeling the higher gear ratio of 18" wheels is compensated partially by lower roll resistance of the tyres.
I’ve also tried 16" x 1,95" tyres (Schwalbe City Jet), these tyres needed a very similar, maybe equal, effort for pedaling like 18" x 1,35" Innovas.
Of course, the effect was different - the Innovas increased speed for ~ 4 km/h.
(The energy was “eaten up” by the higher roll resistance of the City Jets.)
As you own two Stridas now, it might be imaginable to use wide 16" tyres first for training purposes.
Or, change one bike to 18" with Kojak’s for use on flat roads and good weather,
the other 16" Strida could be used if you want to ride hilly roads, when it’s windy and raining.
Btw, Genuine_S wheels are of the same size like the usual Strida 18" wheels (possible tyre sizes for Strida: 32-355 and 35-355) 
Although BSA already answered, I would like to add some info about 18inch wheels etc.
[Wheel] Standard 18inch rim and HED Carbon rim have same diameter, no difference. Weight is also very similar between these 2, but you can reduce weight with break rotor, rimtape, tube and tire. This might help for uphill. (We can go off topic easily with other weight saving mod, so I would stay within “Tire and wheel” in this thread). HED rim has some advantage in aerodynamics although it is hard to tell how much.
[Tire] Panalacer minits lite PT < Kojak < Marathon racer < Marathon Plus
← Lighter and Harder vs Longer life and More confortable ride →
I have never used Continential and IRC tire (for BD-1), but these 2 are also available (in some markets).
[Tube] Schwalbe SV4: 85g, MAXXIS UL-421: 60g
I found that CST is also offering Light Tube, but I have never used.
[Break roter] Original F:107g R:130g / Tektro F:80g R:102g (TR140-4 and TR160-4) / KCNC F:62g / R:74g (* 3rd party 160mm roter for rear has to be filed little bit to enlarge inner diameter). If you sometime have to use your break really really hard, I would not recommend lightest one.
[Other] Rimtape can be swapped with veloplug (veloplug.com/), veloplugs may save some weight, but the real advantage is that it has much much longer life.
If you are interested in weight saving, concerning cost and weight, Tektro roters might be well balanced solution. around 40US$, saves 55g of unsprang weight (if you do not have tool, or if you ask shop to change them it may cost more).
Concerning pure weight, it is obvious that 16inch 24spokes wheel is lighter than 18inch 36 (or 32) spokes wheel, but 18inch has advantage to go faster and has theoretically better ability to deal with bumps. So far, I do not have issue with top gear + 18inch wheel set , so I like 18inch in general, but I do not think everyone should go for 18 inch because people have different purpose and opinion in general.
Good posts
& Great weight infos - Thanks for sharing 
Thank you BSA and Genuine_S for the wealth of information.
I will only upgrade one SD to 18" wheels. It will be for long distances hence the need for larger wheels to cover more distance. I will also fit it with Brooks Flyer since longer distances means longer time sitting upright so a sprung saddle is needed. This will be like my “race-bred” or “touring” Strida.
My original SD will be my everyday commute bike. Since my route is fairly short with some minor climbs.
Different bike for different purpose.