The best method to get rid of background and emotes

Depends on the Market/Gems value.

lowest price is 0.03? -> turn them into gems
any higher? -> sell on market

Don't know much about selling gems, but looking at the price of them, i'd say if you get more than 10 gems for each cent you'd get when selling the item, turn them to gems, otherwise sell the item as it is.
But could be wrong, i don't know that much about it.

If you don't care about getting something for them, make a topic allowing people to claim one each.

I might need to do that soon myself, I got a couple of hundred on one of my alt accounts.

just turn all the $0.03-0.04 trash into gems, every 100 you break (if those items are worth 10 gems) you get a sack worth $1.

you can use steam inventory helper to craft multiple items.

I sell everything. I don't want any gems, as I see them as worthless as the items I want to get rid of.

Wait..what has happened to the market? New update? It now looks like it used to back in the day, where you can choose the seller.

I traded all these stuff into gems and will change later for Bulb Boy booster packs 3 euro each. 8 x 3 euro = 24 euro. Pretty nice profit, but I belive I will have to wait, because currently there are only 7 offers.