Responding to partner's double in Party Bridge
The analysis at bottom was based on an incorrect reading of Opener's first call, as being 1S rather than the current 1C. This doesn't actually change the response structure much, but it does make a big difference in the understanding of what is going on. Before, Opponents were in a confirmed Spade fit and headed to either a nine or ten contract in that suit, with the slight chance of doubling your side for a modest penalty. That's no longer the case, but there are two possibilities.


LHO has made a Strong Jump Shift into 2S

Ouch! Opponents are very likely to get a good score on this hand. The goal is to entice them to try for their slam, while making as few bids as possible on your side, as uninformatively as possible. Then hope they go down one in their slam, or pass on it when it might have made. Be prepared to lose a telephone number if opponents double, but hope that number, but that that number (800, 1100 or 1400) is less than their slam might have been (920 not vulnerable, 1430 vulnerable).

To do this: 


Bid a five card Minor suit if you have one;
Bid a four card Heart suit if you have it; 
Bid a four card minor if you have shortness in any other suit;
Pass - informing partner you have no preference on the escape suit.

LHO has made a Weak Jump Shift into 2S.

This call typically shows 5-9 HCP with a decent 6 card suit containing most of the points. Opener's Redouble suggests they have about 22 points to your side's 18, give or take. The goal is to quickly find a three-level fit where you might get out for down 1 doubled.

To wit:


Bid a five card Minor suit if you have one;
Bid a four card Heart suit if you have it; 
Bid a four card minor if you have shortness in any other suit;
Pass - informing partner you have no preference on the escape suit.



Notice - both bidding structures are the same. Opener's Redouble has removed the burden of a forced call from you, by ensuring Partner another call. Thus you suggest an escape suit only if you have a distinct preference.

Also, in all cases Opener's Redouble is suggesting that their side collect a penalty; but at the cost just noted. It likely suggests a doubleton Spade holding. This means you are not showing values with any call, but just distributional preference. 

To finish, a little follow up:


Pass any and all bids by partner, whether you bid or passed.  
Pass any and all future Doubles Partner might venture. If it is a Double of a slam reached by Opponents assume it is lead directing and act accordingly.
If Partner Redoubles a Double of your suit it is SOS, asking you to choose between the other two suits not being Spades. Making a Takeout Double with a two suiter hand is an abominable call - but somehow partners occasionally decide to do it anyways
If Partner Redoubles his own suit, he is either brilliant or a dunce. In either case Pass and keep out of his way - it's all on him.


And finally, if you end up as Declarer, expect bad breaks and protect against them if you can. For this much action on the hand I expect two or three singletons and voids to show up around the table.



The general agreement, across a wide variety of systems, is that this Redouble will not be left in by your side because Opener has shown a better than minimum hand, probably 16+. (If Opponent's agreement is different, then the following may not apply.)

In consequence, knowing that Partner has asked you to assume a three-suiter, you should make a minimal call in any suit other than Spades precisely when you have a preference. Generally this would mean showing:


a four card Heart suit;
a five card minor suit; or
a four card minor suit with shortness (singleton or doubleton) in either the other minor or in Hearts.


If you fail to make a bid you have assured him that you have none of the hands above, and he will then make a final call for your side based on that knowledge.

The goal in this auction is to quickly find a fit good enough that the opponents are not sure of a set - and so re-enter the auction with a bid rather than a double. It's Poker Time. Keep a straight face; don't agonize over your call; don't give away any tells; and of course don't react to whatever Partner chooses to do.