How to speed up this "translation" query?

I need some expert advice on how to optimize a "translation" query (this
word choice will become clear shortly, I hope).

Say I have a HUMONGOUS table of foreign language "translations" (call it
TRANS) with records like these:

meaning_id: 1
language_id: 5
translation: jidoosha

meaning_id: 1
language_id: 2
translation: voiture

meaning_id: 1
language_id: 5
translation: kuruma

meaning_id: 2
language_id: 2
translation: chat

meaning_id: 2
language_id: 5
translation: neko

meaning_id: 2
language_id: 3
translation: katz

meaning_id: 3
language_id: 4
translation: pesce

meaning_id: 3
language_id: 2
translation: poisson

meaning_id: 3
language_id: 5
translation: sakana

For the sake of this description, let's assume that the records above are
all the records in TRANS (though in fact the number of records in TRANS is
really about ten million times greater).

Now suppose I have a tiny table called INPUT consisting of single text field
(say, word). E.g. suppose that INPUT looks like this:

katz
voiture
pesce

Now, let's fix a language_id, say 5. This is the "target" language_id.
Given this target language_id, and this particular INPUT table, I want the
results of the query to be something like this:

neko
jidoosha
kuruma
sakana

I.e. for each word W in INPUT, the query must first find each record R in
TRANS that has W as its translation field; then find each record Q in
TRANS whose language_id is 5 (the target language_id) AND has the same
meaning_id as R does. E.g. if W is 'katz', then R is

meaning_id: 2
language_id: 3
translation: katz

and therefore the desired Q is

meaning_id: 2
language_id: 5
translation: neko

...and so on.

The only difficulty here is that performance is critical, and in real
life, TRANS has around 50M records (and growing), while INPUT has
typically between 500 and 1000 records.

Any advice on how to make this as fast as possible would be much
appreciated.

Thanks!

G.

P.S. Just to show that this post is not just from a college student trying
to get around doing homework, below I post my most successful query so far.
It works, but it's performance isn't great. And it is annoyingly complex,
to boot; I'm very much the SQL noob, and if nothing else, at least I'd like
to learn to write "better" (i.e. more elegant, more legible, more
clueful) SQL that this:

SELECT q3.translation, q2.otherstuff
FROM
(
SELECT INPUT.word, q1.meaning_id, INPUT.otherstuff
FROM
INPUT
INNER JOIN
(
SELECT translation, meaning_id
FROM TRANS
WHERE translation IN (SELECT word FROM INPUT)
) AS q1
ON INPUT.word = q1.translation
) AS q2
LEFT JOIN
(
SELECT translation, meaning_id
FROM TRANS
WHERE language_id=5
) AS q3
ON q2.meaning_id=q3.meaning_id;

As you can see, there are additional fields that I didn't mention in my
original description (e.g. INPUT.otherstuff). Also the above is actually a
subquery in a larger query, but it is by far, the worst bottleneck. Last,
there's an index on TRANS(translation).