Za list
[infml] Many thanks / Thanks for your letter.
Thank you for your letter.
[fml] We thank you for your letter of 6 September 2001.
[fml] We acknowledge with thanks your letter of 6.9.2001.

Za zaproszenie
[infml] Many thanks for the invitation (to dinner / to your party). I'd love to come and I'm really looking forward to it. // Unfortunately I can't come because...
[fml] Richard Edwards has (great) pleasure in accepting // (greatly) regrets he is unable to accept Susan Stewart's kind invitation to dinner / the kind invitation of the Cultural Attache to a reception / Mr and Mrs David Banks' kind invitation to the wedding of their daughter.
Jan Kowalski
lub
[fml] Richard Edwards thanks for his/her/their kind invitation to..., which he has pleasure in accepting // which he regrets he is unable to accept (due to a previous engagement).
Jan Kowalski

Za prezent
Thank you very much for...
[infml] Many thanks / Thank you (ever) so much for the delightful present / for the lovely flowers.
[infml] You really shouldn't have (bothered). / It was really sweet / kind of you. It's just what I wanted.

Za pomoc / datki
I am most grateful for / I greatly appreciate all the trouble you have taken (on my behalf).
[infml] Jim and I cannot thank you enough for helping us out.
[fml] Please accept / May I offer you our warmest thanks for your valuable assistance.
[fml] I would like to offer you on behalf of the department our most sincere thanks / grateful thanks for your generous donation.

[fml] - formal [infml] - informal