I have a vector layer being rendered in QGIS.
I want to delete various features in the layer. I'm currently deleting each node by selecting the node through node tool and then pressing the delete button.
But I want to delete very large portions in the map. Using this method will cause a lot of time.
Is there any other method where I can draw a polygon around the feature which needs to get deleted and delete them easily?
Use the select tool (either select by rectangle or select by polygon) to select the features you want to delete. Then you can delete all of them by hitting the delete button on the tool bar.
Use Edit > Select > Select Features by Polygon. Draw a polygon to surround the features you want deleted. (Left click for each point then right click to close your polygon.) 
Click Layer > Toggle Editing. 
Click Delete Selected from the Editing toolbar. 
.
Note: This process deletes all the selected features. I'm not sure how to select and delete only a certain node/vertex within a feature.
Layer > Toggle Editing is disabled, save the features as a new file (right click the layer name in the Layers panel, select Export > Save Features As...) which will unlock the ability to delete features. Then proceed as @maning has described.
Using a Select Features by ... tool and pressing delete will work most of the time.
However, you can run into a problem where you try to delete a feature using the Delete Selected tool and it doesn't let you. This will happen if, for example, you are attempting to delete the last two nodes in a line feature part.
If you want to delete a feature part by selecting and deleting nodes, you need to use the Advanced Digitizing toolbar:
Delete Part Tool:
