How to create connection between AWS VPC and my PC/LAN?

This is not odd at all and very common. One easy way to do that is to use an vpn solution, e.g by deploying an openvpn VM from an openvpn AMI (almost everything is configured by default), or by installing another vpn solution on one of your instance. Then, you will only have to log to this vpn and you will be able to resolve your instances with their private IP addresses

However, if you do want your instances to be routed between your LAN/VPC, this is slightly more complicated. you may have to consider using a more complex architecture, still based on VPN but with "Virtual Private Gateway / customer gateway" configuration

Best self-explanatory YouTube Video for installing OpenVPN for this you need to use AWS Marketplace AMI - OpenVPN

In addition to running OpenVPN on AWS you could also use a VPC Virtual Private Gateway.

http://docs.aws.amazon.com/AmazonVPC/latest/UserGuide/VPC_VPN.html

You would set up a deice on your side (usually the router or firewall) and connect it to the VPC via a VPN tunnel to an Amazon VPN endpoint. This solution would make it easy to add multiple hosts on your LAN to the DS without having to connect them all via individual VPN connections.

Edit: This popped up again so I thought I'd add I did a writeup on using Pritunl for something like this a couple months after posting this answer. I've been managing Pritunl Enterprise since then and with ~150 users daily or so it's been performing wonderfully even with just t2.medium hosts and another for the Mongo database.

https://www.nathanv.com/2015/11/09/pritunl-for-aws-vpc/