I am trying to make NGINX as standalone web server for static content. I am able to achieve download (GET) of files from NGINX. However, I am getting error 301 when I do post and 405 when I tried PUT. Can someone please advise configuration that allows me to upload files using PUT or POST ?

location /static/data {
alias /static-data/;
client_body_temp_path /tmp/;
client_body_in_file_only on;
client_body_buffer_size 128k;
client_max_body_size 100M;
autoindex on;
}

POST and PUT by definition are NOT static methods.
Your question contradicts your initial statement of wanting to serve static content.

I agree with you.. So my requirement is to upload binary files from one source (through HTTP PUT / POST) which can be served to other clients (via HTTP GET)