What are some ways to increase damage resistance?

You're not going to achieve the same level of damage resistance without power armor as you will with it. However, there is more to it than just the perks available on the perks screen, throughout the wastelands and the buildings in it there are a variety of books, here are some that I've found so far that will help:

Collectable books:

• Astoundingly Awesome 3 - Take 5% less damage from robots
• Astoundingly Awesome 5 - +5 poison resistance
• Astoundingly Awesome 10 - +5 radiation resistance
• Wasteland Survival 2 - Take 5% less damage from insects
• Wasteland Survival 8 - Take 5% less damage from melee attacks

Note that all of these "5% less damage taken" perks aren't included in your overall damage resistance rating, but the specific damage type resistance ratings are showing on the STAT > STATUS screen in Pip Boy.

Then you've got your perks:

• Toughness - +10 damage resistance per level
• Unstoppable - +1% chance to avoid all damage per level

From there you're looking at building up every piece of your armor to resist as much damage as possible. But you should know, even with the armor I've found so far I'm nowhere near power armor levels.

Ballistic Weave goes a very long way to offsetting this gap.

You can unlock the Ballistic Weave upgrade after joining the Railroad - once you've been given access to HQ, you'll meet P.A.M., a robot that offers randomly generated 'radiant' quests. One of these quests is named Jackpot, in which you'll be sent to clear out a random location to secure a D.I.A. Cache.

After completing the quest, the next time you speak to Tinker Tom, he'll tell you about Ballistic Weaves, and begin selling clothing with them implemented. Furthermore, if you have the Armorer Perk, you'll be able to craft and install them yourself.

With max-rank Armorer, you'll be able to make Ballistic Weave Mark V, which adds +110 to both ballistic and energy defense. You can apply this upgrade to a variety of clothing and hats, including, most notably, to a handful of 'light' clothing pieces that offer stat upgrades, but can be worn under regular armor, such as Army Fatigues, Military Fatigues, the Minuteman Outfit, and several others.

With Ballistic Weave Mark V in both a piece of light clothing, and a hat such as a Battered Fedora, you'll have +220 to both defenses before armor. Upgraded Combat Armor in all five slots should add another 60-75 defense at a minimum, and once you start finding heavy armor, that number can go well over 100, bringing you over 325 before considering any sort of perks or magazine buffs.

It's no T-45, but it should put you in pretty good shape for exploring the wasteland.