#(doch)

-> same as "eben"

doch: "Ich dachte, wir können den Kuchen auf den kleinen Teller stellen."

"Das ist doch ein großer Kuchen!"

-> As we both know, the cake is big and I want you to reconsider what you said earlier based on that. (doch often implies shared knowledge and a correction)

doch/nur/bloß: "Ach hätte ich doch/nur/bloß ein großes Stück Kuchen!"

-> If only I had a big slice of cake!

wohl: "Warum kommt sie mit einem LKW zur Feier?"

"Es ist wohl ein großer Kuchen."

-> I'm assuming it must be a big cake, then, going from the information we have right now. (I'm using "es" not "das" bc it's implied the speaker hasn't seen it yet) In this case it's a joke.

ja: "Das ist ja ein großer Kuchen."

-> stress on "das": I'm surprised by how big this cake is! And I feel neutral to happy/pleased/positive about that.

or "Das ist ja ein großer Kuchen."

-> stress on "ist": Emphasising that I think we both know that the cake is big.

or similarly: "Das ist ja ein schöner Kuchen, aber viel zu groß!"

-> I'll hand it to you, that cake is nice, but come on, it's way too large! (speaker is using 'ja' to start with an appeasing statement, before disagreeing/giving a new consideration)

einmal/mal: "Das ist mal ein großer Kuchen!"

-> What a pleasant surprise, this is a big cake for once. (Speaker is being nice here)

aber: "Das ist aber ein großer Kuchen."

-> stress on "das": I'm surprised by how big this cake is!

schon: "Das ist schon ein großer Kuchen."

-> Despite what anyone else might say, that cake is big.

denn: "Ist es denn ein großer Kuchen?"

-> I'm especially interested whether the cake is big 👀

vielleicht: "Das ist vielleicht ein großer Kuchen!"

-> Wow, that is one big cake!

Imperatives:

doch: "Bestell doch einen Kuchen."

-> Why don't you order a cake? (speaker gives more or less obvious advice)

halt: Bestell halt einen Kuchen!

->Just order a cake. It's the obvious solution.

mal: Bestellst du mal einen Kuchen?

-> I can't order a cake myself right now, so could you do it for me?

or

-> Could you finally order a cake, please? We're waiting. (especially: "Bestellst du endlich mal einen Kuchen?")

eben:

eh: "Nimm dir doch ein Stück. Ich würde mich freuen und der Kuchen ist eh zu groß."

-> Come on, take a slice. I'd be happy and the cake is too big, anyway.

ruhig: "Fang ruhig an zu essen."

-> Go ahead, you can start eating. I really don't mind.

schon: Fang schon an zu essen!

-> Eat something already!

ja: Und bring ja Kuchen zur Feier mit!

-> You had better bring cake to the party!

Additional meanings that weren't covered in the previous examples:

schon: Wie groß kann der Kuchen schon sein?

-> How big can the cake be? (speaker is implying the cake can't be all that big -> implies irrelevance)

schon: Den Kuchen wird schon keiner essen.

-> Despite your/anyone's worries, I don't think anyone will eat the cake.

Combinations:

Yes! You can combine them to your heart's content!

"Das ist ja vielleicht mal ein großer Kuchen!"

Is a perfectly normal sentence in spoken German. And it means:

"That is yes maybe once a big cake."

"Wow, that is one big cake!"

I might write a follow-up post on how exactly to combine them! Although you can find it all in the book "Modalpartikeln und ihre Kombinationen" by Maria Thurmair. [2]

Literature

[1] Fabian Bross: German modal particles and the common ground. (PDF; 1,6 MB). In: Helikon. A Multidisciplinary Online Journal, 2, 2012, S. 182–209. https://www.researchgate.net/publication/230881580_German_modal_particles_and_the_common_ground