I am planning a one week visit to Olympic national park for next summer. My husband & I love hiking and we want to see all the areas of the park. Would it be convenient to use crescent lodge as our base and take day trips to the other areas or should we spend a couple of days in each lodge?

Had to check the map to see where you were going.
http://www.olympicnationalparks.com/peninsula-maps.aspx
It looks like Crescent would be good for the northern part of the park. Maybe 1 or two nights at Lake Quinault would work better for seeing the southern parts of the park.
Remember to bring your passports in case you want to take the ferry over to Victoria from Port Angeles.

We just returned and we stayed at night at each lodge. It all depend on what and where you want to do it at.

Our favorites were
Sol Duc Falls
Hurricane Ridge
Rialto Beach to Hole in the Wall hike at low tide for tidepools

click on my name and you will find a recent trip report with a lot of photos.

We love to hike and are particularly fond of moderate to strenuous hikes. Are there enough of those? Which area is the best for that. We should probably spend a couple of nights there? How far from seatac? Is it best to start north and travel south or the other way around?

I don't really think it matters which direction. You are 2 hours or so from Seatac. You might consider doing a Whale Watch tour and/or spending a couple of days on San Juan Islands too.

Yes, there are plenty of serious hikes. Oddly, for Olympic National Park, some of the short ones are really nice too.