Is there any way to increase your carrying weight with max strength and power armor?

Solution 1:

There are a few ways that you can increase your max carry capacity, some temporary and some permanent.

Permanent perk solutions (these are only feasible in your current situation if you have a spare perk point and the required SPECIAL stats)

1. Strong Back (6 STR required): You can get +25/+50 carry capacity for the first 2 ranks of this perk, if you don't have it yet. Also, if you are not on the new Survival difficulty, the 4th point in this perk allows you to fast travel while over-encumbered.
2. Lone Wanderer (3 CHR required): If you are traveling with a companion and have this perk, dismiss them for an instant +50/+100 carry weight increase, depending how many points you have in the perk. For extra weight relief, trade with them and fill up their inventory with items from your inventory before sending them off.

Temporary Solutions

Any consumable that gives you temporary Strength will also temporarily increase your carry weight. Each point of strength from the consumable will give you 10 carry capacity, per the Fallout Wiki. Moreover, some of these can stack, according to this answer. Consumables that increase strength include:

1. Beer (STR+1)
2. Bobrov's Best Moonshine (STR+1)
3. Bourbon (STR+1)
4. Dirty Wastelander (STR+3)
5. All Gwinnett Beers/Iced Gwinnett Beers (STR+1)
6. Poisoned Wine, Wine (STR+1)
7. Rum (STR+1)
8. Whiskey (STR+2)
9. Buffout (STR+2)
10. Buffjet/Bufftats/Psychobuff (STR+3)
11. Mysterious Serum (STR+5)
12. X-Cell (STR+2)

Grilled Radstag also gives a direct +25 to carry capacity. However, unless you grilled some beforehand or have radstag meat and a cooking station nearby, that won't help you out.

Outside of consumables, there are also a couple of tricks that can help you carry more when in an over-encumbered situation.

1. You can drop your heaviest item and 'carry' it. After dropping the heaviest item from your inventory, you can hold down the 'interact' button while looking at it to pick it up and hold it out in front of you. It will not count against your carry weight. And, if by doing this you go below the max weight threshold, it will allow you to run somewhere where you can store your items.
2. If with a companion, there is a sort of exploit that allows them to carry unlimited weight. Per the Fallout Wiki page on companions:

All companions can carry an unlimited quantity of loot: rather than trade with them, place the items you want them to carry on a dead body or in a storage container then command them to to grab anything worthwhile. You can also make them pick up items laying on the ground one item at a time.

Other long-term solutions

After you get out of your current predicament... There are some other things you can do to ensure this doesn't happen again. Outfitting your equipment with Pocketed or Deep Pocket (+5/+10 on arm/leg pieces, +10/+20 on chest) can also help with your carry weight. However, as you've stated you are using power armor (and your standard armor mods are not active while you are in power armor), modifying your power armor leg pieces with the mod Calibrated Shocks will give +50 carry capacity per leg, so +100 with the mod on both legs.

You can also determine your companion, should you travel with one, to be more focused towards carry capacity. Per the Fallout Wiki, Strong and Danse have the highest carry capacities of the companions, at 200 and 210 respectively. Other companions have a limit of 150.

• Outfitting companions with 'Pocketed' or 'Deep Pocketed' modded equipment will also increase their carry weight.
• Live & Love issue #3 increases companion carry capacity by 10.
• Dogmeat does not count as a companion when determining bonuses from the Lone Wanderer Perk. You can, therefore, raise your carry capacity by 100 (and get all other bonuses of this perk) while traveling with Dogmeat (who has a carry capacity of 150, for an overall net gain of 250 weight between the two of you).

If you have the fallout-4-automatron DLC, robot companions can also be a great source of extra carry capacity. Most notably, robot companions with the Sentry Bot arms & legs offer the greatest carry weight boost. The equivalent Protectron pieces offer a decent increase in their carry capacity, and requires lower perk thresholds to use on your robot companion (per a few sources).

Console Solutions

If you are playing on PC, you have access to the console. If you don't mind using it in your playthrough, carry weight can be modified using the following command (replace xx with the number you want your carry capacity to be increased by):

player.modav carryweight xx

You can also use player.setav. However, modav will modify your current carry weight capacity by the value you enter. This allows you to 'reset' your carry weight later, should you want to, by using the negative of the value you chose.

Solution 2:

Take all ranks of strong back,the sprinter perk that reduces sprint cost by half and both leg armor upgrades. Use legendary gear that increases ap regeneration.

You will never need to drop a thing.

I am running around the wasteland carrying over 200000 pounds of stuff.