Multiday backpacking trip linking up trails to do a North/ South loop(ish) of sorts from Staircase / North Fork Skokomish TH. Original plan was to link to Six Ridge and up to Flapjack Lake then out, but due to dead battery chargers and the rumored tough nature of Six Ridge, I exited at Lake Irely TH. Full trip was:
Day 1: Staircase Campground to Marmot Lake (via N. Fork Skokomish / First Divide / Home Sweet Home / Duckabush) 21mi / 5,925 gain
Day 2: Marmot Lake to Dose Forks (via O'Neil Pass / Anderson Pass) 20.17mi / 2,972 gain
Day 3: Dose Forks to Three Forks (via Gray Wolf Pass) 21.43mi / 4,852 gain
Day 4: Three Forks to Hayes River (via Cameron Creek / Cameron Pass / Lost Pass / Hayden Pass) 25.25 mi / 6,234 gain
Day 5: Hayes River to Lake Beauty (via Low Divide / Skyline Trail) 20.33mi / 5,407 gain
Day 6: Lake Beauty to Three Lakes 15.38mi / 3,797 gain
Day 7: Three Lakes to Lake Irely TH + FSR walking  9.58 mi /420 gain

TL;DR:
The Olympics are rugged. If you're used to cruiser trail miles and pace, toss that out the window when you're hiking in the Olympics. These trails are a constant rinse and repeat cycle of piney, rooty trail, rocky creek bed trail, water crossings, rocky trail, muddy drainage, brushy, overgrown, a handful of blowdowns, and back again. Also, the olympics are slippery when wet. See below for any notes that vary from the above. You get a lot of variety on these trails, and the views at the passes are stunning and make every hard mile worth it. Weather was perfect, and so many ripe berries, and also lots of bear sightings!  

Road Conditions: Great! Paved all the way to the junction to Staircase and then very smooth gravel road. This is a campground, so there are several toilets, trash bins, and information center. 

Trail Conditions: 
North Fork Skokomish River Trail: Same as summary above. Was EXTREMELY humid. Traps heat and moisture. Crowded/popular trail. More brushy/blowdowns the further down you go.

Home Sweet Home: Same as summary above. A bit more technical and rocky near first divide. Between here and Duckabush were some wasp nests. 

Duckabush River Trail: From Home Sweet Home to Marmot Lake. It got notably more brushy and technical closer to the lake. Same note about wasp nest. Marmot Lake/Hart Lake has gorgeous views and great little camp spots.

O'Neil Pass Trail: Same as summary above. Ridge trail more on the brushy side. Saw 6 bears within 3 miles of Marmot Lake (2 just near camp). All feasting on berries. 

East For Quinault Trail / Anderson Pass: Trail from junction to Anderson Pass. Couple creek crossings, no problem. Nice grade and trail up to Anderson Pass. 

West Fork Dosewallips: Same as summary above. This was probably the most cruiser trail of them all, which some brush and muddy drainage in spots. 

Dosewallips Trail: Same as summary above. This was probably the most cruiser trail of them all, which some brush and muddy drainage in spots. 

Gray Wolf River Trail / Gray Wolf Pass: Same as summary above. This was more brushy and more blowdowns on the north side of the pass going down to three forks. A few creek crossings but had foot logs. Climb up and down pass was a little more steep but not bad.

Cameron Creek Trail: Same as summary above. This trail is deceptively STEEP! it will be rolly and cruiser then suddenly short steep up and downs, and gradual climb to the pass. It was much slower going than I imagined. A creek crossing with no foot log about 3 miles in. About shin deep and easy to pass. Lots of up and down getting to the basin and pass. The climb up to the pass is a scree switchback but manageable and well packed from previous hikers. The views at this pass are INCREDIBLE!

Lost Pass: Same as summary above. More brushy and a few blow downs, fairly easy ridge trail and no scree to get there. the south side of lost pass to Dose Meadows camp is Toe-Jamming/Calf Burning STEEP! I was coming down and wowzers, the grade is unforgiving, but thankfully short lived. Going up I can imagine would be pretty slow going as well. Tread is fine and only a few blowdowns but trail is otherwise fine.

Hayden Pass Trail: Same as summary above. This trail is more gradual climb, with a little scree at the top, but this switchbacks are large and sweeping, so less steep than Cameron. The back side down to Elwah River is looooonnnggg gradual descent/climb. I was descending and it felt like forever until I was off this trail. There are some views and you go through an old burn area. Most notably this section had lots of muddy drainage sections. 

Elwah River Trail: From Hayes River/Hadyen Pass Junction to Low Divide. Similar to summary but more brushy and there's a river ford that just deep enough to get your feet wet. A few areas where the trail seems to end, but there's a large log to cross on a dried up creek bed, and little flags if you look. My shoes were still in decent shape until this day. Legs got scraped up and muddy shoes. Pretty flat and quick though. 

Skyline Trail: This trail is the most unique of them all. Get on your pack, and hop on a stair stepper if you want to prepare for this trail. It doesn't seem like much if you look at the overall gain/loss for your day, but you will hit steep up and downs in and out of the creek chutes. This is slow-going trail with lots of brush (read CAR WASH). You get a lot more rocky technical trail here too. There's a section that is similar to the enchantments that just all rock and you have to follow rock cairns. Aside from this section there's no actual loss of trail or route/navigation. Just a few narrow spots where trail has washed out a bit, and the steep up and downs. The views are so stunning though, and a couple more bear sightings along here as well. If you're a hiker/backpacker who only likes pristine trail, I'd steer clear of this one. If you're used to a little bushwhacking and like a challenge, this trail is so worth it and not that bad in my opinion.

Big Creek Trail: Same as summary above. This trail is aptly named as you dead end on the trail at a big creek. There's a couple logs you can cross or downclimb some rocks and cross, but be warned, the log is SLIPPERY at the end next to the rocks. I took a spill and hit my face on the rocks and found myself upside down dangling over the water. Amazingly nothing lost, and only a few scrapes, but aside from this the trail is rocky and a little brushy. Also, Irely Lake is pretty dried up, not much "lake" there. 

Animals/Bugs: Not a ton of bugs or enough to be problematic. I still managed some bites from my stay near the Elwah River. There are a TON of yellow jackets. I didn't find them aggressive or problematic, but if you stand still and close your eyes you will hear a constant hum/buzz of them flying around everywhere you go. I saw 8 bears. 2 very close surprises right off trail, so keep your head up. Lost of bears in the meadows feasting, and honestly surprised I didn't see more. I heard elk bugles 3-4x but never saw any. Some chunky cute marmots, and other birds, and forest critters. Notably lots of frogs! I don't feel like I see them often, but saw quite a few on this trip.

Water sources: Water was never an issue on this trip. I can't even think of a dry section as there's little streams and creeks. Maybe the furthest you would go without it would be maybe a 3 mi stretch, and that's assuming you can't collect from a small trickle somewhere. 

Other: Berries were ripe and delicious! Nice little snack as you walk through the wilderness. Pretty empty trails aside from the first day, and second day near Anderson Pass. 

Happy Trails!