I play bass in a three-piece indie/post-hardcore band. I'm trying to find ways to create a fuller sound when our guitarist plays leads and solos. Currently, I usually either achieve this by playing chords/arpeggios, or using effects (current setup includes a chorus, a delay, a distortion, an overdrive and a guitar multi-effect that's used mainly as an octave pedal), and I'm just wondering if anyone has any other suggestions, especially any somewhat-cheap pedals you'd recommend. I just want to avoid following the same formula of "Oh, he's soloing, better turn on the distortion and play powerchords" by finding a lot of ways to create a full sound.
It really sort of depends on the set-up of guitar player and drummer and the frequency ranges that they occupy; and the type of lines you're actually playing. Personally I like to boost the upper mids a fair bit and dig in. You can achieve a sort of aggressive guitar/bass hybrid sound that really does fill up a lot of space this way. Think Geddy Lee/Chris Squire etc.
Spare a Cow
Eat a Vegan
I like two-handed tapping for filling space in a bass role. Low note E string with a higher up power chord/any other diad works great, or tapped arpeggios.

Another thing I like is slap and pop, or just slapping the notes you want. The aggressive clanging really stands out and helps fill the space left by the guitarist's absentee riff.

What does your drummer do during the solos? more cymbalwork could help too with filling extra sonic space
Well; it ain't cheap (US$300.00), but the Aphex Aural Exciter/Optical Big Bottom can work near miracles in that area.
"Maybe this world is another planet's hell?" - Aldous Huxley
You want to fill up the sound but sometimes it's nice to keep a bit of sonic room too - like in Know Your Enemy by RATM. Get tight with those drums and dig in!

But also, check out Fury by Muse for a big fat bass tone. Some distortion and synth on there (as ever). And moving your way from the root to the octave via fills (like in the chorus) helps too!

Good luck! I might be in your position soon
My band just recently became a 3 piece (happened in the middle of a tour too, that sucked) and I've learned that playing power chords while the guitarist is playing leads or soloing works pretty well.

I usually play the chords higher on the neck and try to emulate what the rhythm guitarist was doing. It also helps if you add a little bit of grind and drive in your tone.
I have no idea, as I don't have this problem in my trio band.

Our guitarist never plays solos.
I do them on bass instead.
I started using an Exotic EP boost, check it out.
It works. I'm getting a bigger full sound, liven's up everything.

Disclaimer: I have no affiliation to Exotic or any other gear manufacturer's. I've wondered sometimes if there are users here with ulterior motives, but I digress.